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• Orbit maneuver-free approach to the angle-only relative orbit determination for is proposed. • The angles-only orbital observability problem is solved by introducing radial basis function neural network to capture the nonlinearity of the perturbed dynamics. • The RBFNN frame including training data acquisition, data pre-processing, and the network design for angles-only orbit determination problem is developed. • The validity of the proposed algorithm is evaluated by numerical simulations. • The anti-noise, generalization performance, and the sensitivity of the solution are checked. Angles-only orbit determination during space situational awareness missions for non-cooperative targets such as space debris is subject to the well-known observability problem, that is, the orbital state is weakly observable or even unobservable because of missing range measurements. The key point to solve this problem is how to quickly capture the nonlinearity of orbit dynamics if only one space-based passive sensor is available to observe the target and translational maneuvers are not executed. To solve the short-arc angles-only problem, this study develops a simple and fast orbit determination method by exploiting the advantages of radial basis function neural network (RBFNN). Emphasis was placed on the design of the RBFNN, which was trained to construct a mapping network model from line-of-sight (LOS) measurements to the relative orbit. First, the perturbed relative orbit dynamics considering the Earth's non-spherical J2 term and air drag was established with the LOS measurement model. Second, a RBFNN-based angles-only orbit determination frame was developed, in which the generator of the training dataset, data preprocessing algorithm, and RBF network structure were designed. Finally, the proposed method was verified and tested using a set of numerical simulations of low-Earth orbit cases. The anti-noise and generalization performance of the designed network and the sensitivity of the solution accuracy to the measurement frequency and span were presented and discussed. Additionally, the advantages of the RBFNN-based method were confirmed by comparison with the results obtained using the BPNN (Back Propagation Neural Network)-based method. The simulation results show that the average orbit prediction error for LEO scenarios is approximately 0.08% using the index of initial relative distance, where only three sets of LOS angles are measured within a span of 24 s. [ABSTRACT FROM AUTHOR]

Satellite Laser Ranging (SLR) technology is one of the main technologies in the field of space geodesy, it has played an extremely important role in laser ranging data application and research. As a commonly used geodynamic satellites, the main contribution of LAGEOS and LAGEOS-2 is the solution of orbit determination and station coordinates. At present, there are 8 analysis centers of the International Laser Ranging Service (ILRS) to release the precise orbit products for the two LAGEOS satellites. However, there is currently no relevant research on the analysis of the consistency of these orbits. So, the authors would evaluate the accuracies of them, and the results show that the orbital accuracies of the two LAGEOS satellites are 3 ∼ 5 cm. SLR is regarded as one of the important input data of the International Terrestrial Reference Frame (ITRF), the analysis center of ILRS provides weekly solutions of station coordinates for ITRF. But, due to the limitation of SLR observation conditions, for example most observations of Chinese SLR stations can be made at night, and laser ranging test cannot be conducted in rainy days, the orbit solution of the seven-day arc may have the problem of less data. Therefore, this paper proposed a method for computing the station coordinates based on long arc orbit determination, and we developed the LAODGEO software (Long Arc Orbit Determination Software for Geodynamic Satellite), which is used to solve the orbits of two LAGEOS satellites and station coordinates of five SLR stations in China. The results show that the obtained orbital precision is basically superior to 3.70 cm, and the 3DRMS values between station coordinates solved by us and the coordinates published by SLRF2014 are mostly smaller than 0.013 m, which is consistent with research results domestic and overseas. [ABSTRACT FROM AUTHOR]

• A Hp-Adaptive Pseudospectral Hybrid Optimal Algorithm is proposed. • The optimal solution of the OSIP and OPEG problem can be robustly solved by this work. • Cases with different thrust configurations and initial conditions are reported. In this paper, a Cartesian model of the orbit pursuit-evasion game under J2 perturbations is constructed, and a step-by-step solution method applicable to this problem, namely the Hp-Adaptive Pseudospectral Hybrid Optimal Algorithm, is proposed by analyzing the principle of the pseudospectral method and the costate mapping principle. We first use the hp-adaptive Radau pseudospectral method to solve the one-sided interception problem to obtain a tentative guess of the costate and then get the saddle-point solution of the game problem by solving the two-point boundary value problem through the Newton method. The numerical results show that the hybrid method proposed in this work can efficiently find the optimal trajectory of interception and the optimal control laws of the game problem and have high accuracy. In addition, the effects of J2 perturbations and the initial orbital altitude of the evader on the game results and the algorithm itself are discussed in this paper. [ABSTRACT FROM AUTHOR]

• A relative orbit design method for CubeSats flying around space station is proposed. • The CubeSat's relative orbit is used for observing feature-points on surface of space station. • The design method considers the field-of-view constraints and occlusion effect. • The method could be used for other similar constrained close-range on-orbit service missions. This paper presents a novel relative orbit design method for CubeSats flying around the space station to perform visual inspection considering the Field-Of-View (FOV) constraints and occlusion effect. Firstly, a parametric model for Periodic Relative Orbits (PROs) is established by using the well-known Clohessy-Wiltshire equations. Based on this model, the relative orbit design problem for orbital target inspection is successfully integrated into a problem of two-parameters determination, one of which is the correlation coefficient and the other is the orbital amplitude. Secondly, by categorically evaluating the range of design variables, the design method for generating feasible solutions of PROs to satisfy the FOV constraints is proposed. Thirdly, considering the existence of the occlusion effect of large space structure, this paper presents an efficient calculating method to evaluate the degree of occlusion based on the analysis of line-of-sight blockage. Then, to avoid the occlusion effect, an improved relative orbit design method is developed. Finally, the designed algorithms are testified by carrying out some typical simulations with the China Space Station as the observed object and a small CubeSat assumed to perform the required inspection mission. The results illustrate well the validity and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

• A novel guidance algorithm for drag-modulated aerocapture is presented. • The algorithm is compared in detail to an efficient implementation of the state of the art solution, a numerical predictor-corrector, and is shown to achieve equivalent targeting performance for significantly lower computational expense. • This contribution could thus meaningfully advance the near-term technical feasibility of drag-modulated aerocapture. Aerocapture is a method of achieving orbit insertion via a single pass through the atmosphere of the central body. Single-event jettison drag modulation is a simple way of achieving control during atmospheric flight by effecting a discrete change in the aerodynamics of the vehicle. A novel guidance algorithm, energy reference guidance, is developed and implemented for a reference scenario of a small satellite aerocapture demonstration at Earth, and is compared to the baseline numerical predictor–corrector solution. The new approach is shown to achieve equivalent apoapsis targeting performance as the baseline algorithm with significantly lower CPU demand during atmospheric flight, although more onboard memory is required in exchange. The relationship between targeting performance and required memory is quantitatively explored for the new algorithm; the selected configuration generates approximately 3.3 MB of data, which is expected to be well within the capability of relevant avionics systems. [ABSTRACT FROM AUTHOR]

To realize rapid, safe and optimal avoidance for spacecraft in complex threat situations and incomplete-information conditions, and considering the problems in existing hierarchical decision-making modes, a learning-based spacecraft reactive anti-hostile-rendezvous (AHR) maneuver control framework is proposed in this paper. First, a fundamental AHR action planner based on the interfered fluid dynamical system (IFDS) is proposed, in which the avoidance strategies for hostile and non-adversarial threats are appropriately integrated. An avoidance strategy matched with the IFDS is further designed by specifically considering high-intensity confrontation situations where a threat maintains persistent pursuit. Then, the "state-action" solution methods based on deep reinforcement learning (DRL) and multi-agent-DRL (MADRL) methods for orbital avoidance maneuvers are proposed to control the avoidance time and directions by optimizing the IFDS parameters. In the offline training stage, the DRL method will first simulate the interactive processes between the spacecraft and non-adversarial threats so that the spacecraft can gradually adapt to complex space environments and generate the relative primary avoidance maneuver strategies. On this basis, for hostile threats, the MADRL-based solution method of orbit game strategies is further established, in which the spacecraft and hostile threats are constructed as two types of opposite agents to simulate the game processes so that the strategy levels can be bilaterally evolved and the AHR success rates can be improved. After training, the corresponding neural networks are extracted from the agents in the DRL-based and MADRL-based methods for reactive AHR maneuver control. Moreover, a progressive agent training mechanism matched with the above DRL-based and MADRL-based solution methods is proposed, which can reduce the invalid interactions in initial training episodes, improve the training efficiency, and enhance the generalization ability of orbital game strategies. Finally, the effectiveness of the proposed framework is demonstrated by simulations. [ABSTRACT FROM AUTHOR]

We showed that isomorphism classes of idempotent evolution algebras are in bijection with the orbits of the semidirect product group of the symmetric group and the torus, considered the combinatoric problem of enumeration of isomorphism classes for these algebras over arbitrary finite fields, derived a general counting formula, and obtained explicit formulas for the numbers of isomorphism classes in dimensions 2, 3, and 4 over any finite field. [ABSTRACT FROM AUTHOR]

Classical methods for initial orbit determination (IOD) include Laplace method, Gauss method, and their variations. In addition to this, based on the characteristic of optical observation data nowadays, experts propose some other IOD methods, like Double- r method and admissible region method. One of the ways to determinate the orbit through double- r method is to guess distances of the target from the observer at two epochs—usually at the first and the last one. By doing so, we can solve the Lambert problem, and use its solution as the initial guess of the orbit. Furthermore, we can improve the initial guess by iterations to reduce the root mean square (RMS) of the observations. The admissible method is based on the concept of attributable (longitude, latitude, and their rates). With some conceptions, the admissible region described by the range and range rate from the observer is characterized. Using triangulation we can find the nodal point that makes the RMS minimal. In our work, we apply one intelligent optimization method—the particle swarm optimization method to the two methods, based on simulated and real data, and compare the results with that of modified Laplace method. At last, we briefly discuss the possibility of applying the double- r method to the orbit link problem. [ABSTRACT FROM AUTHOR]

The "IADC space debris mitigation guidelines" requires that the post-mission orbit lifetime of low Earth orbiting (LEO) satellites should not be longer than 25 years, which is the key to debris mitigation. To analyze the degree of global compliance to this 25-year guideline, a fast and relatively accurate orbit life estimation algorithm is required. The traditional method uses numerical orbit propagation to accomplish the task, although its accuracy is high when a high-precision force model is used, the calculation is time-consuming. This paper proposes a new method for orbit lifetime estimation without relying on orbit propagation. A back propagation (BP) neural network is used to directly fit the relationship from the satellite parameters to the orbit lifetime. The space objects that have reentered the Earth's atmosphere are selected from the catalog database of the US Space Surveillance Network (SSN), and are used to generate samples for network training. The genetic algorithm is combined with the traditional back propagation algorithm for the training of the neural network. The results show that for the specific application background of identifying whether a satellite complies with the 25-year guideline, the orbit lifetime estimation accuracy of the BP network meets the demand to some extent. Moreover, because it does not involve orbit propagation, the BP network has a high computational efficiency in estimating orbit lifetime, showing a good application prospect. [ABSTRACT FROM AUTHOR]

We present precise spectrophotometric parameters of the two close visual binary systems, HD 200325 and HD 220077, which have not been spectrophotometrically studied before. Precise parameters are presented based on Al-Wardat's method for analyzing binary and multiple stellar systems. Which combines the spectroscopic analysis with the photometric analysis to construct the combined synthetic SED and its components of a binary with the aid of Kurucz's models. From the analysis of the synthetic models, we determine precise values for each of the spectrophotometric parameters, masses, and parallaxes of the systems. Precise spectrophotometric masses of both components were found to be M sph A = 1.30 ± 0.12 M ⊙ and M sph B = 0.85 ± 0.08 M ⊙ for HD 200325 and M sph A = 1.08 ± 0.10 M ⊙ and M sph B = 0.90 ± 0.10 M ⊙ for HD 220077 with an age of about 1.413 ± 0.10 Ga and 3.548 ± 0.35 Ga, respectively. Also, the orbital parameters are modified based on Tokovinin's method for solving orbits of binary stars. In our spectrophotometric and dynamical analysis, we arrive at new dynamical parallaxes as π dyn = 18.8096 ± 0.80 mas for HD 200325 and π dyn = 12.681 ± 0.48 mas for HD 220077. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the quantum channels that preserve and also separate the orbits of pure states under the action of a group unitary representation π. Such a quantum channel will be called π -orbit injective. We prove that for finite group and complex Hilbert space cases, such a channel necessarily separates all the pure states. However, this is no longer true for quantum channels acting on real Hilbert spaces, or quantum channels acting on complex Hilbert spaces with (infinite) compact group representations. In both cases, we obtain necessary and/or sufficient conditions under which the quantum channel is orbit injective. These conditions are given in terms of the so called property (H) of characters (more generally, irreducible representations) of the group, and characterizations of property (H) are presented for real and complex valued multiplicative characters. [ABSTRACT FROM AUTHOR]

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed "HASDM-ML," "CHAMP-ML," and "MSIS-UQ" machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called "consider covariance sigma point (CCSP)" filter that can account for the density uncertainties during orbit propagation. As a test-bed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions. [ABSTRACT FROM AUTHOR]

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver. [ABSTRACT FROM AUTHOR]

Recently, large LEO constellation satellites have received much attention from the aspect of Space Domain Awareness (SDA) due to their significant number and relatively complex orbit states. Low-thrust propulsion system technologies are widely used during the lifetime of such satellites, making it difficult for the work of TLE (Two Line Element) based maneuver detection. This study proposes a machine learning method for orbit state classification based on TLE data, considering the concept of the Auto-Encoder (AE) network and Decision Tree (DT). In this manuscript, the orbit states were classified into four categories: non-maneuver, controlled orbit raising, controlled orbit lowering, and controlled orbit maintenance. First, historical TLE data of multiple satellites of the STARLINK constellation system and uncontrolled objects in a similar orbital area was analyzed using an Auto Encoder network to identify nonlinear features. Second, the extracted feature was sent to the DT network for the training of the supervised classification model, which could classify the input into four categories of orbit states. Finally, extra targets that had not been considered during the modeling process were used to test the applicability of the proposed method on satellites of the same constellation system. The results suggest that the method we presented here was applicable for orbit state classification with a macro precision of 93.8% and a macro F1-score of 93.7%, according to our numerical experiments. Once set up, the proposed method presented a feasible orbit state classifier for satellites of the same constellation system, operating at a similar altitude. [ABSTRACT FROM AUTHOR]

In view of the limitation of ground-based Tracking Telemetry and Command (TT&C) system in covering the geostationary satellite in space and time, the method of determining the orbit of the geostationary satellite by the LEO (Low Earth Orbit) multi-satellites network with small orbit inclination was proposed. According to the space environment and optical viewing conditions, the simulation data were screened to simulate the real observation scene. The precise orbit determination (POD) of geostationary satellite was calculated by using the optical angle measurement data and the numerical method. By comparing with the reference orbit, under the condition of platform's orbit accuracy of 5 m, measurement accuracy of 5-arcsecond, and 12 hours of observation, the POD accuracy of geostationary satellite by two LEO satellites can reach the order of kilometers, while the POD accuracy by four LEO satellites can reach the order of 100 meters. Therefore, the POD accuracy has been greatly improved with the increase of the number of LEO satellites. [ABSTRACT FROM AUTHOR]

• An analytical solution for initial orbit determination (IOD) based on the bistatic radar is derived using two observations at different times. • The accuracy is evaluated by geometric dilution of precision (GDOP) analytically derived by the linearization approximation. • The performance of the method is investigated for space objects under different observation geometries. An analytical initial orbit determination (IOD) method using two observations from a bistatic radar is proposed. Each observation contains bistatic range and the doppler frequency shift, azimuth angle and elevation angle. This problem arises from the challenging catalogue process for small space debris, which features sparse radar observations. By incorporating doppler measurements into the original Lambert's IOD problem which uses two position vectors and can only be solved iteratively, we show that an analytical solution can be obtained. The specific angular momentum conservation equation and the specific mechanical energy equation are used as kinematic constraints. An ad hoc coordinate system is proposed to derive the solution. The geometric dilution of precision (GDOP) metric is analysed to express the IOD accuracy using a linearization method. Simulations are carried out to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The optimal low-thrust linearized elliptic orbit rendezvous problems are studied for both continuous thrust and piecewise constant thrust considering the communication window constraint. Based on the analytical state propagation expressions for linear relative motion under on–off constant thrust, the analytical energy-optimal solution using piecewise constant thrust is derived by the Lagrange multiplier method for given switching time points. This solution is further extended to obtain the analytical energy-optimal solution using continuous thrust. For the piecewise constant thrust with free switching time points, the fuel-optimal problem is formulated as a nonlinear programming problem, which is solved by a modified differential evolution algorithm. In addition, the derived analytical energy-optimal solution for given switching time points is used to reduce the number of optimization variables, and it is numerically proven to effectively reduce the optimization time. Several examples are presented to show the effectiveness of the proposed method for the low-thrust orbit rendezvous problem considering the communication window constraint. • The analytical energy-optimal solution for piecewise constant thrust is derived. • The analytical energy-optimal solution for continuous thrust is derived. • A new method is presented to reduce the optimization time for fuel-optimal problem. [ABSTRACT FROM AUTHOR]

Precise orbits are required for real-time precise point positioning (PPP). Nowadays, real-time orbit corrections with respect to broadcast ephemerides are normally transmitted to the users with an update interval between 5 and 60 s. Due to time latency, users extrapolate to calculate the satellite positions at the needed epochs. However, since the original satellite orbits change rapidly, users have to extrapolate the orbit corrections. Nevertheless, the correction accuracy of GLONASS decreases faster over time than GPS, Galileo, and Beidou, in addition, the calculation efficiency of the satellite position seems not perfect. In this study, an improved polynomial fitting method was proposed to improve the orbit extrapolation ability of polynomial by introducing the satellite velocities and accelerations into the fitting model. Experimental results of GPS, GLONASS, Galileo, and Beidou show that the accuracy of extrapolated orbits could be within a few centimeters when the time latency is approximate 10 min and 40 min for eclipsing and non-eclipsing satellites, respectively. And these results also have been confirmed through the PPP experiments from eight global distribution stations with multi-GNSS observation data on 2019–1-1. Thus, by utilizing the new method, it is possible to directly extrapolate the original satellite orbits, which suggests that the application of real-time precise orbits can be independent of broadcast ephemeris. [ABSTRACT FROM AUTHOR]

• A novel initial orbit determination method for optical track association is presented. • The role of the orbit determination in the track-to-track association is discussed. • Proposed methods for optical and radar tracks are compared against classical alternatives. The detection and identification of Resident Space Objects (RSOs) from survey tracks requires robust and efficient orbit determination methods for the association of observations of the same RSO. Both Initial Orbit Determination (IOD) and Orbit Determination (OD) methods perform the orbital estimation in which the association of tracks relies. The choice of proper IOD and OD methods is essential for the whole data association, since they are in charge of providing the estimation required to evaluate the figure of merit of the association. In this paper, we review the state of the art and propose a novel method that does not require initialisation, accounts for measurement noise and provides a full estimation (i.e., state vector and covariance) from an arbitrary number of optical observations. To do so, a boundary value problem is formulated to find a pair of ranges leading to a minimum residuals of the observations. The proposed methods are compared against classical alternatives simulated in scenarios representative of the current space debris environment. [ABSTRACT FROM AUTHOR]

• Structure and properties of LPO families are studied by mapping approach. • Periodic families, which bifurcates from vertical and halo orbits are constructed. • A modified bounding planes method is used for the generation of LPOs. • The applicability area of the bounding planes method is presented. In the framework of circular restricted three-body problem the libration point orbits form the families of periodic and quasi-periodic solutions. In the paper, the mapping of initial conditions is utilized to describe and study the structure and properties of these families. A new numerical method for orbit generation, which is applicable both for the periodic and quasi-periodic orbits, is provided and explored. The applicability area of the proposed method is constructed and analyzed for the vicinity of Sun-Earth L1. Based on the comprehensive numerical investigation of this area, the xz -maps aligning the initial conditions of the orbits crossing this plane perpendicularly with their properties were constructed and analyzed. The quasiperiodic Lissajous and quasi-halo orbit families appears on these maps as the domains surrounding the curves corresponding to periodic halo and vertical families. Accurate analysis of these domains made in possible to study the structure of resonant k -periodic families, which bifurcate from halo and vertical orbits. The initial conditions of these families are presented by the curves, which thread the quasi-halo and Lissajous domains. These k -periodic families are computed up to k = 10 for the resonant orbits bifurcating from the halo family, and up to k = 25 for the resonant orbits bifurcating from the vertical family. Some examples of such orbits different provided. The maps of initial conditions illustrate several important properties of the libration point orbit families, and can be useful for mission design as a tool to select the orbit fitting the mission requirements. [ABSTRACT FROM AUTHOR]

It is necessary to keep the constellation with high accuracy and high stability in a space-based gravitational wave observatory. Few orbital maneuvers are carried out in the science mode, which puts forward higher requirements for the initial constellation condition. The orbit determination method for the space-based gravitational wave observatory is mainly studied in this paper. Firstly, the orbit determination accuracy requirement of the space-based gravitational wave observatory is analyzed. And then, an orbit determination method based on an extended Kalman filter is designed to improve the orbit determination accuracy by using inter-satellite range and angle measurement information. • This paper solves the problem of high-accuracy orbit determination for a space gravitational wave observatory. • The orbit determination accuracy requirement of the space-based gravitational wave observatory is analyzed. • A high-accuracy orbit determination method using inter-satellite range and angle measurement information is designed. [ABSTRACT FROM AUTHOR]

• A new mathematical model is established for hyperelastic shells with both structural damping and dynamic loads. • The Melnikov method combined with numerical calculations is first introduced for the strongly nonlinear system. • Quasiperiodic oscillations, limit cycles and chaos with the damping are found. • Thickness parameter has opposite effects on the system nonlinearity for different equilibrium points. This paper investigates the effects of dynamic loads and structural damping on the nonlinear behaviors of incompressible hyperelastic spherical shells modeled by the Yeoh strain energy function. Firstly, the dynamical modeling is formulated for the nonlinear behaviors of the shells by the variational principle, and the second order nonlinear ordinary differential equation describing the radially symmetric motion is obtained. Then, the dynamic behaviors, such as periodic, quasiperiodic and chaotic motions, are discussed under different loading types. Particularly, for constant loads, the first integral of the integrable Hamiltonian system without damping is given and it is numerically proved that there exists an asymmetric "∞" homoclinic orbit for the prescribed material parameters obtained in experiments; moreover, it is found that for different prestretches, the structural parameter has a completely different role on the nonlinearity of the system, and the basins of attraction are given with the structural damping. For periodic loads, there exist some interesting dynamic phenomena, i.e., quasiperiodic oscillation in the approximately integrable Hamiltonian system, limit cycles and chaos with the damping. The criterion for chaos is discussed by the Melnikov method combined with the numerical calculation and the chaos is further analyzed with the Poincaré section and the phase plane. [ABSTRACT FROM AUTHOR]

Presented within this work is a new method for inertial orbit estimation of an object, either known or unknown, adaptable to a network of low-cost observation satellites. The observation satellites would only require a monocular camera for line of sight measurements. Using the line of sight measurements of each observer, a pair of orthogonal geometric planes that intersect both the observation satellite and the target are created. The intersection of the two planes in the inertial frame defines the new measurement model that is implemented with multiple observation nodes. Total system observability is analyzed and the instantaneous observability (per node) is used to remove "bad" measurements from the system. The measurement model is used in an extended Kalman filter framework and the measurement noise nonlinear transformation is addressed. Two cases are presented: first, a small number of observation nodes is analyzed to highlight the use of the instantaneous observability and its deleterious effect on the filter performance. Then, the method is expanded out to multiple observation satellites in a constellation. For both cases, the results show that this method is capable of producing accurate orbit estimation that converges in a short time. • Accurate, fast converging, inertial orbit estimation. • Based only on line of sight angle measurements. • Pair of orthogonal geometric planes intersecting both the observer and the target. • Application to a constellation of observation nodes. • Measurement covariance undergoes a nonlinear transformation. [ABSTRACT FROM AUTHOR]

Guidepost-based navigation system is a novel autonomous orbit determination method for the GEO satellite. The system is achieved by using the camera imaging function to obtain the guidepost images and the GNSS signal receiver to obtain the pseudoranges between the GEO and the navigation satellites. Due to the high altitude of GEO satellite and the time-varying sunlight condition in the space environment, it may be difficult to obtain object image points and the distance measurements of GNSS because of the weak visibility of the guideposts. To deal with the problem, a novel integrated orbit determination system is presented. The Earth landmarks, the in-orbit spacecraft and GNSS navigation satellites whose line-of-sights and the distance can be easily obtained are used at the same time as information for the GEO satellite navigation based on the observability conditions analysis. The observability of the GEO satellite navigation system is analyzed through the physical observability, the mathematical observability and the engineering observability through the observing geometry, the rank of observability matrix and the Cramer-Rao lower bound (CRLB) respectively. Besides, the maximum correntropy unscented Kalman filter (MCUKF) algorithm is applied to improve the estimation stability of the system in the presence of non-Gaussian noises. The simulation indicates the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

A three-impulse point return orbit design method is proposed for the manned lunar high-latitude exploration mission. First, considering the restrictions of the reentry corridor and the landing point simultaneously, the constraint conditions of the point return orbit are analyzed. Second, a serial orbit design strategy is presented. In the initial calculation, by decoupling the three-impulse transfer and the lunar escape, a two-segment patched method based on the pseudo-perilune parameters is proposed to determine the three-impulse point return orbit. The three-impulse transfer segment is backward designed by combining maneuvering at the special points with the Lambert problem in the hybrid orbit model, while the lunar escape segment is forward solved by introducing a comprehensive conic method. In the accurate solution, the result of the initial calculation serves as the initial value to perform the backward and forward integration for two segments in the high-fidelity model, respectively. The simulation examples verify the effectiveness and feasibility of this strategy, and show the advantages of high accuracy of the initial calculation and low velocity increment consumption. Finally, a large amount of simulations are conducted by applying this strategy, and the orbit characteristics are discussed. The research conclusions can provide a reference for the design of the point return orbit scheme for the manned lunar exploration mission. • Two-segment patched method for designing the three-impulse point return orbit. • New three-impulse transfer method with low impulse consumption. • Comprehensive conic method for generating the lunar escape segment. [ABSTRACT FROM AUTHOR]

The rising interest for space activities within the so-called "New Space Economy" has led in the past few years to a substantial increase of satellites launches, making space more and more populated, especially in the LEO region, where most of the newly conceived missions are supposed to operate. This phenomenon is imposing the need of an improvement and augmentation of the current space surveillance systems, possibly implementing high-capacity and passive methodologies capable of exploiting standard satellite radio-frequency transmissions. This paper describes and analyzes the performances of a satellite orbit determination method based on Time Difference of Arrival (TDOA) measurements, collected by means of a radio stations network. The analysis is aimed at assessing the influence of a variety of parameters on the orbit estimate accuracy, in order to determine whether this method can be used effectively to support and contribute to current space tracking techniques. [ABSTRACT FROM AUTHOR]

We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, we consider the recently introduced methods of the difference and the ratio of the LDs of neighboring orbits, as well as a quantity related to the finite-difference second spatial derivative of the LDs, and use them to determine the chaotic or regular nature of ensembles of orbits of a prototypical area-preserving map model, the 4-dimensional symplectic standard map. We compare the characterization obtained by these LDs-based diagnostics against that achieved by the Smaller Alignment Index method of chaos detection, by recording the percentage agreement P A between the two classifications. We also study the influence of the final number of orbit iterations T , the order n of the indices, as well as the distance σ of neighboring orbits on the performance of these methods, and find appropriate T , n and σ values which allow the efficient use of the three indices as short time and computationally cheap chaos diagnostics achieving P A ≳ 90 %. Our findings clearly indicate the capability of LDs to efficiently identify chaos in systems whose phase space is difficult to visualize, due to its high dimensionality, without knowing the variational equations (tangent map) of continuous (discrete) time systems needed by traditional chaos indicators. • Presentation of chaos diagnostics based on computations of Lagrangian descriptors. • Identification of chaos in high dimensional symplectic maps. • Comparison of various efficient chaos detection techniques. • Identifying chaos without using variational equations or tangent maps. [ABSTRACT FROM AUTHOR]

In this work, we consider the Toda flow associated with compact/Borel decompositions of real, split simple Lie algebras. Using the primitive invariant polynomials of Chevalley, we show how to construct integrals in involution which are invariants of the maximal compact subgroup, and moreover, we show that the number of such integrals is given by a formula involving only Lie-theoretic data. We then introduce the space of Hessenberg elements, characterize the generic Hessenberg coadjoint orbits, and show that the dimension of such orbits is precisely twice the number of nontrivial invariants which appeared earlier. For the class of classical, real split simple Lie algebras, we construct angle-type variables which in particular shows that the Toda flow is Liouville integrable on generic Hessenberg coadjoint orbits. • We study the Toda flow on Hessenberg elements of real, split simple Lie algebras. • Nontrivial invariants of the maximal compact subgroup K in involution are constructed. • The formula for the number ν of such K-invariants involves only Lie-algebraic data. • Dimension of generic Hessenberg coadjoint orbits = 2 ν. • Toda is integrable on generic Hessenberg orbits for the classical simple Lie algebras. [ABSTRACT FROM AUTHOR]

In this paper we establish the existence of canonical coordinates for generic co-adjoint orbits on triangular groups. These orbits correspond to a set of full Plancherel measure on the associated dual groups. This generalizes a well-known coordinatization of co-adjoint orbits of a minimal (non-generic) type originally discovered by Flaschka. The latter had strong connections to the classical Toda lattice and its associated Poisson geometry. Our results develop connections with the Full Kostant–Toda lattice and its Poisson geometry. This leads to novel insights relating the details of Plancherel theorems for Borel Lie groups to the invariant theory for Borels and their subgroups. We also discuss some implications for the quantum integrability of the Full Kostant Toda lattice. • New links explored between dual groups of Lie groups and their Poisson geometry. • Dixmier–Pukanszky operator of Plancherel theory related to Toda invariant theory. • Canonical coordinates established for symplectic leaves of full Toda systems. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to show a method to find orbits near artificial equilibrium points for a satellite equipped with a continuous thrust that allows it to stay near the poles of a celestial body. The physical system includes the presence of a moon of the celestial body under observation, and the perturbation caused by this moon is counteracted by an algorithm to help the satellite to stay close to its original position, instead of escape from it. The equations of motion are changed under some approximations, and analytical solutions for these equations are obtained and analyzed. Initial conditions are used such that their secular terms are nullified. These solutions are restricted to a short period of time, but we propose a method in which there are periodic updates in the thrust. Thus, the solutions can be extended for the duration of the mission. A numerical simulation is obtained, whose results are required to be in agreement with the analytical solution using these periodic adjustments of the thrust. This agreement means that the motion of the spacecraft remains bounded close to its initial position for longer times. Several systems with different sizes and mass parameters are used to show the results of the research, like Sun-Earth-Moon, Sun-Ida-Dactyl, Sun-Saturn-Titan and Sun-Mars-Phobos systems. The results also indicate the locations of points that require minimum magnitude of the thrust. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples. • We provide a novel MPC design with guaranteed economic performance for dynamic/periodic nonlinear constrained problems. • Naive/Alternative formulations for dynamic/periodic case do not yield desirable performance guarantees. • A novel design procedure for terminal ingredients for economic dynamic operation is presented. • We demonstrate performance benefits for a periodic time-varying HVAC system and a time-invariant nonlinear CSTR system. [ABSTRACT FROM AUTHOR]

For the p -Sylow subgroups U of the finite classical groups of untwisted Lie type, p an odd prime, we construct a monomial C U -module M which is isomorphic to the regular representation of C U by a modification of Kirillov's orbit method called monomial linearisation. We classify a certain subclass of orbits of the U -action on the monomial basis of M consisting of so called staircase orbits and show, that every orbit module in M is isomorphic to a staircase one. Finally we decompose the André-Neto supercharacters of U into a sum of U -characters afforded by staircase orbit modules contained in M. [ABSTRACT FROM AUTHOR]

The autonomous navigation of multi-satellite systems using only on-board measurements is a fundamental task in many space missions. The main purpose of this study is to establish new methods for the autonomous orbit determination of a dual satellite system using relative position measurements only. A novel concept, k -order local weak observability, is proposed. Based on unperturbed Kepler orbit dynamics and J 2 -perturbed orbit dynamics respectively, sufficient and necessary conditions of k -order local weak observability are mathematically proved for the autonomous navigation system. Observability-based modified EKF, modified UKF, and modified SDREF are presented and used as navigation algorithms. Simulation results illustrate the performance of the developed navigation algorithms in comparison with the traditional EKF, UKF, and SDREF. • Two satellite orbits are determined mostly with relative position measurements. • Observability rank condition is subdivided into k-order local weak observability. • Observability degree of nonlinear systems is indicated on-line in the filtering procedure. • Performance of navigation are improved with observability-based modifications. [ABSTRACT FROM AUTHOR]

Periodic orbits are important keys to understand the motion of a massless particle in the vicinity of a binary asteroid system. Due to the complex gravity generated by the irregular-shaped asteroids, it is difficult to generate periodic orbits with an analytical method, except with the linearized dynamics in a small region around the libration points. This paper has presented a numerical method to search the three-dimensional periodic orbits in a global space. The grid searching method is used to find nearly periodic orbits, and then the shooting method is used to get the accurate periodic orbits. The method is applied to the binary asteroid (66391) 1999 KW4 to solve the periodic orbits in the vicinity. The periodic orbits are then classified into five categories according to their shapes and locations. The search method can also be used to find periodic orbits in the vicinity of other binary systems. • A global search method for periodic orbits about a binary asteroid is introduced. • Both the primary and secondary are modeled as a homogeneous polyhedron. • Periodic orbits near binary (66391) 1999KW4 are searched as a demonstration. • The periodic orbits are classified into five categories by their characteristics. • The period, stability, and application prospect of periodic orbits are analyzed. [ABSTRACT FROM AUTHOR]

Frozen orbits are ideal options for global mapping and observation. In this paper, a design and maintenance method of frozen orbit is presented and applied to the small body exploration. On the basis of the Legendre addition theorem, an analytic solution of the frozen orbit is developed, which can obtain frozen orbits with arbitrary orders of zonal harmonic coefficients in concise forms. Based on the proposed method, the distribution and properties of frozen orbits around Vesta are discussed. Then, an anti-chattering self-adaptive control law is proposed to maintain the frozen orbits in a high-fidelity environment. The control law is proved to be stable and robust against model uncertainties and unmodeled perturbations. Simulation results show that the proposed method can obtain the frozen orbit efficiently with desired performance, while the self-adaptive control law can keep the orbit stable with satisfactory fuel consumption. This study provides a new option for frozen orbit design in future exploration missions. [ABSTRACT FROM AUTHOR]

Exact solution of spherical mean-field plus a special orbit-dependent non-separable pairing Hamiltonian with multi non-degenerate j -orbits, which is related to two previously known hyperbolic Gaudin models, is explored. It is shown that the Hamiltonian with suitable constraints on the pairing interaction parameters turns to be exactly solvable. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe-Gaudin-Richardson ansatz equations of the solution for any number of pairs k are determined. It is shown that the pair excitation energies can be calculated more easily than those of the separable pairing model studied previously. As examples of the solution, pairing excitation energies with the number of pairs up to the half-filling in the ds -shell with 3 j -orbits and in the pf -shell with 4 j -orbits are presented and compared with those of the mean-field plus the general separable, the special separable, and the standard pairing models. It is shown that the pairing excitation energies of the model are close to those of the mean-field plus special separable pairing or general separable pairing model. [ABSTRACT FROM AUTHOR]

• Discussion of analytical orbit contraction methods and their shortcomings. • Extension of King-Hele method for semi-analytical propagation considering drag. • Introduction of a superimposed, parametric atmosphere model. • Verification against numerical quadrature and non-averaged integration. • Increase of accuracy considering atmosphere models with variable scale heights. Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used method of semi-analytically integrating trajectories of objects subject to atmospheric drag was proposed by King-Hele (KH). However, the analytical KH contraction method relies on the assumption that the atmosphere density decays strictly exponentially with altitude. If the actual density profile does not satisfy the assumption of a fixed scale height, as is the case for Earth's atmosphere, the KH method introduces potentially large errors for non-circular orbit configurations. In this work, the KH method is extended to account for such errors by using a newly introduced atmosphere model derivative. By superimposing exponentially decaying partial atmospheres, the superimposed KH method can be applied accurately while considering more complex density profiles. The KH method is further refined by deriving higher order terms during the series expansion. A variable boundary condition to choose the appropriate eccentricity regime, based on the series truncation errors, is introduced. The accuracy of the extended analytical contraction method is shown to be comparable to numerical Gauss-Legendre quadrature. Propagation using the proposed method compares well against non-averaged integration of the dynamics, while the computational load remains very low. [ABSTRACT FROM AUTHOR]

This study proposes a high-precision fixed-thrust free return orbit design method for a manned lunar mission centred on the rendezvous and docking with the lunar space station. Future manned lunar landing missions based on the lunar space station will require different spacecraft to achieve rendezvous and docking with it in different mission stages. Adopting the perilune parameters to design the Earth–Moon flight trajectory would be more convenient for decoupling in this kind of series missions. Thus, a new set of pseudo-parameters representing the perilune motion states is defined, and based on these, a hybrid multi-conic method is then proposed to design the free return orbit for manned spacecraft. The new method is more accurate than the traditional four-phase patched-conic method, and can produce initial values with a higher converging speed for a high-precision trajectory iteration design. Then, a fast and high-precision continuation method for the fixed-thrust trajectory is proposed based on the impulse-based solutions, and the gravity loss of the impulse-thrust transfer is analysed. Finally, the general characteristics and launch window of the free return orbit, as well as the reachable domain of the pseudo-perilune parameters, are analysed using the hybrid multi-conic method. The results will provide a theoretical basis for future missions planning. • New set of perilune pseudo-parameters for perilune motion states is defined. • Hybrid multi-conic method for designing free-return orbit. • High-precision fixed-thrust continuation method for impulse transformation. [ABSTRACT FROM AUTHOR]

Being the simplest case in the three-body problem, the motion of a test particle in the field of two fixed bodies was first considered by Euler in 1760. In celestial mechanics, it represents the motion of a spacecraft that is attracted by two celestial bodies fixed in space and do not influence each other. The motion of the spacecraft is influenced by the gravitational forces of these two fixed bodies. Although the scenario of having two centers fixed in inertial space is not practical, some orbits could be applied in actual missions. This paper considers the above situation with a focus on closed orbits around a body such as a dumbbell-shaped asteroid or a binary body. The aim of this study is to demonstrate a robust method to obtain these orbits. Two types of conceivable motion around two fixed bodies are considered: an elliptic orbital motion and an 8-shaped motion. This paper analyzes the characteristics of these motions, where the mass ratio of the celestial bodies and the distance between them are taken as parameters. • The motion of the spacecraft around two inertially-fixed bodies is considered. • A closed orbit of the spacecraft with a rotation number of one is focused. • The conditions required for the lemniscate and planetary motion are elucidated. • Various orbits are systematically obtained by determining a certain parameter. • The analytically obtained orbits are validated by numerical simulations. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the on-orbit servicing (OOS) of geosynchronous satellites based on low-thrust transfers while considering the different demands of the satellites and the effects of perturbations. One or more servicing spacecraft start from a parking orbit and service the satellites in sequence via low-thrust orbit transfers, and return to the parking orbit in the end. The different demands lead to different service requirements of time and mass, while the perturbations affect the control solution of servicing spacecraft during each transfer, and induce orbit drifts of uncontrolled target satellites during the mission. An analytical method that can efficiently calculate the fuel consumption of low-thrust transfer is proposed, and methods for evaluating the orbit drifts of uncontrolled satellites are presented. The impact of perturbations on OOS mission is investigated in detail, showing that non-negligible factors include lunisolar attraction and tessral harmonic. Based on the dynamic models, a string-based simulated annealing algorithm is adopted to schedule the OOS mission. The efficiency of the proposed dynamic models and optimization method are verified through ample simulations. Results show that it is much more efficient and reasonable to take orbit drift calculations as corrections on the scheduling result assuming no orbit drifts. The proposed models and methods make it possible to schedule the OOS mission with low-thrust transfers, while achieving high accuracy under the effects of J2 perturbation, lunisolar attracion, tesseral harmonic and solar radiation pressure. • On-orbit servicing (OOS) of GEO satellites via low-thrust transfers is studied. • Analytical transfer solution is developed to calculate the fuel consumption. • J2, lunisolar attraction and tesseral harmonic affect fuel consumption of OOS. • Various servicing demands lead to different requirements of time and cargo mass. • A string-based simulated annealing algorithm is designed to schedule the OOS mission. [ABSTRACT FROM AUTHOR]

A method to deduce orbit solutions of predetermined accuracy with respect to a reference orbit is presented. The idea is to guarantee the applicability to all orbits and provide both the orbit and the covariance matrix with a constrained method error. Such a solution may be useful, if different users expect different levels of accuracy or have limited privileges to access high-precision data. The method proposed in this paper performs a non-linear least squares fit to the catalogued reference orbit with an modified force model. Subsequently, that solution is subjected to an ephemeris compression method and the results thereof can be provided to the users in terms of Chebyshev polynomial coefficients, after being put in a standardised data message. One of the main advantages is that there is no need for a propagation on the user's side anymore. The orbit information is obtained directly from the series representation in the data message for any time in the in the provided interval. Moreover, the orbit theory used in the orbit determination and catalog maintenance is not required to be shared or synchronized with the community any longer. • New method to provide orbits with predetermined accuracy. • Allows to have different orbit solutions in terms of levels of accuracy. • Envelope function to compress covariance information. • Analysis of envelope function in the collision probability computation. [ABSTRACT FROM AUTHOR]

Abstract Using mainly variational methods and an approximation technique we obtain one homoclinic orbit for a Hamiltonian system type (P) u ̈ + V u (t , u) = 0. Our approach allows us to consider new examples of nonlinearities which do not satisfy the classical Ambrosetti–Rabinowitz condition and neither strict growth hypotheses that allow to use Nehari Manifold. For instance, in our system we can consider a periodic potential V given by V (t , u) = − 〈 L (t) u , u 〉 + f (t) | u | 2 ln (1 + | u |) , which clearly does not verify those conditions when L (t) is positive definite and symmetric matrix and f is a nontrivial nonnegative continuous function. We notice that f may vanish in some part of its domain. [ABSTRACT FROM AUTHOR]

Abstract An exact solution of nuclear spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j -orbits is presented. The extended one-variable Heine–Stieltjes polynomials associated to the Bethe ansatz equations of the solution are determined, of which the sets of the zeros give the solution of the model, and can be determined relatively easily. A comparison of the solution to that of the standard pairing interaction with constant interaction strength among pairs in any orbit is made. It is shown that the overlaps of eigenstates of the model with those of the standard pairing model are always large, especially for the ground and the first excited state. However, the quantum phase crossover in the non-separable pairing model cannot be accounted for by the standard pairing interaction. [ABSTRACT FROM AUTHOR]

We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers. [ABSTRACT FROM AUTHOR]

Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth’s albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions. For the considered orbits, first-order relativistic contributions give accelerations of about 20  nm/s 2 and are dominant in the radial direction. [ABSTRACT FROM AUTHOR]

Most of the CubeSats have a volume range from 1U to 3U, which limits their applications due to the difficulty of miniaturizing payloads. To facilitate the needs on a larger but low-cost satellite platform, the AOXiang (AOX) project has been developed by Northwestern Polytechnical University (NPU). The primary objectives of AOX project are four-folds: 1) To demonstrate the world first 12U CubeSat Star of AOXiang and 12U orbit deployer which uses an innovative electromagnetic unlocking technology. 2) To investigate the feasibility of using polarized sunlight for spacecraft attitude determination and navigation, and perform microgravity research using a miniaturized gravimeter. 3) To test a fault tolerant on-board computer using the System On the Programmable Chip (SOPC) technology, and 4) To gain the experience from developing the CubeSat and the subsystems. The CubeSat was launched in June 2016. Now, the mission has achieved all the goals. This paper provides the detail information of the AOX project, with a focus on the introduction of the subsystems of the 12U CubeSat, the orbit deployer and the payloads. The recent in-orbit results of the first NPU are also presented. In addition to the educational objective that has been reached with more than 50 young scholars and students participated in the project. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of infinitely many homoclinic orbits for a class of first order Hamiltonian systems z ̇ = J H z ( t , z ) , where the Hamiltonian function H ( t , z ) is nonperiodic in t and only locally defined near the origin with respect to z . Under some mild conditions on H , we show that these Hamiltonian systems possess a sequence of homoclinic orbits near the origin. [ABSTRACT FROM AUTHOR]