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In this paper, we present a novel integrated method for designing nonlinear stiffness systems based on a general spring-boundary model (GSBM) to study the number of mechanical configurations for nonlinear stiffness systems designed by the combination of a linear spring with a nonlinear boundary. GSBM consists of a lumped mass, a special-shaped track, a roller rolling in the track and GLSM with either positive or negative stiffness. The integrated method considers pre-tensioned, pre-compressed and original length conditions of GLSM to design roller trajectories to customize nonlinear stiffness systems. It is proved that the mechanical configurations of nonlinear stiffness systems designed by the combination of a linear spring with a nonlinear boundary are not limited to one, but six or eight forms: for systems with nonnegative or nonpositive potential energy, there are six independent mechanical configurations, and for other systems, there are eight independent mechanical configurations., Comment: 10 pages,7 figures. arXiv admin note: substantial text overlap with arXiv:2303.05108

Nonlinear systems exist widely in nature, however, how to construct systems with accurate expected non-linearity artificially is still a problem, which greatly limits their experimental study and engineering application. In this paper, we present a general nonlinear mechanical model (GNMM) based on special-shaped cam-spring mechanism (SCSM). GNMM consists of a mass, a roller, a track and a novel general spring model (GSM). Firstly, the equation of motion is derived and compared with that of SCSM. Then, the roller trajectory functions for arbitrary given continuous force are derived. Finally, Duffing system with softening non-linearity is constructed as a design example. The results presented herein show that GNMM has a more general restoring force than SCSM, and prove that there are at least six independent mechanical configurations for a given nonlinear system with continuous restoring force., Comment: 10pages,7figures

Dual-energy computed tomography has great potential in material characterization and identification, whereas the reconstructed material-specific images always suffer from magnified noise and beam hardening artifacts. In this study, a data-driven approach using dual interactive Wasserstein generative adversarial networks is proposed to improve the material decomposition accuracy. Specifically, two interactive generators are used to synthesize the corresponding material images and different loss functions for training the decomposition model are incorporated to preserve texture and edges in the generated images. Besides, a selector is employed to ensure the modelling ability of two generators. The results from both the simulation phantoms and real data demonstrate the advantages of this method in suppressing the noise and beam hardening artifacts., Comment: 40 pages, 10 figures, research article

This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and Laplace vectors with a free injection point. Trajectory optimization with the pseudospectral method and nonlinear programming are supported by the initial guess generated from the Chang-Chichka-Marsden Lyapunov-based transfer controller. This approach successfully solves several low-thrust optimal problems. Numerical results show that the Lyapunov-based initial guess overcomes the difficulty in optimization caused by the strong oscillation of variables in the Cartesian coordinates system. Furthermore, a comparison of the results shows that obtaining the optimal transfer solution through the polynomial approximation by utilizing Cartesian coordinates is easier than using orbital elements, which normally produce strongly nonlinear equations of motion. In this paper, the Earth's oblateness and shadow effect are not taken into account.