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A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, that is, the Pluto–Charon, Earth–Moon, Sun–Jupiter, and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes. [ABSTRACT FROM AUTHOR]

This paper presents a skip entry guidance algorithm that uses a numerical predictor–corrector and a patched corridor for low-lifting capsules returning from the Moon. The longitudinal and lateral channels are assumed to be decoupled. The bank angle magnitude profile is parameterized using piecewise linear segments with respect to a normalized energy. The shape of the bank-vs-energy profile is determined using a single piecewise-defined variable. The predicted longitudinal bias is nullified using a false position method. The adverse effects of aerodynamic and atmospheric uncertainties are mitigated using an on-board estimating strategy during the trajectory prediction. A patched corridor is devised to manage the lateral state based on analytical derivations and reasonable approximations. The sign of the bank angle is reversed when the boundary of the patched corridor is violated. Dispersed simulations are implemented in a three-degree-of-freedom dynamical context, and the results demonstrate the high performance of the proposed guidance algorithm under stressful testing conditions. [ABSTRACT FROM AUTHOR]

A skip entry guidance algorithm blending numerical predictor-corrector and nominal trajectory tracking is presented for lunar return vehicles. The guidance is decoupled into longitudinal and lateral channels. A piecewise bank-vs-energy magnitude profile and a sign profile are adopted in the skip phase. A magnitude parameter is used to adjust the predicted downrange, and a pseudo-crossrange at the beginning of the final phase is selected as the lateral control variable. Prediction biases of both channels are nullified by a false position iteration algorithm. An on-line estimation and modeling method is introduced to compensate for aerodynamic and atmospheric uncertainties. A nominal trajectory for the final phase is generated based on actual reenter conditions, and the obtained nominal trajectory is tracked by a linear feedback law. A lateral corridor is used to manage the lateral state. The proposed guidance algorithm is assessed using three-degree-of-freedom Monte Carlo analyses, and the results show a satisfactory and robust performance under highly stressful dispersions. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problems of multiple reaction–diffusion memristive neural networks (MRDMNNs) with known or unknown parameters and switching topologies via distributed control. In complex environment, the proposed system may face switching topologies, diffusion effects, external disturbance, parameter mismatch or uncertainty, so designing security control laws to synchronize the proposed system is a enormous challenge. The parameter mismatch terms herein are extended to be unbounded, which is different from the general boundedness hypothesis. Since the parameter mismatch term would be known or unknown, we design a novel parameter-dependent controller for the known condition and a novel parameter-independent adaptive controller for the unknown condition respectively. By constructing new Lyapunov functions, using some properties of M-matrix and robust control method, the synchronization errors will all converge into a bound set via the two designed nonlinear controllers. And we are able to select appropriate control parameters to control the upper bound. Moreover, the obtained theorems can determine the feedback control gains, which can be used for security control. Finally, two numerical simulations are given to support the obtained theoretical results. [ABSTRACT FROM AUTHOR]