The orbital dynamics equation of a spacecraft around an irregular sphere small body is established based on the small body’s gravitational potential approximated with a tri-axial ellipsoid. According to the Jacobi in...The orbital dynamics equation of a spacecraft around an irregular sphere small body is established based on the small body’s gravitational potential approximated with a tri-axial ellipsoid. According to the Jacobi integral constant, the spacecraft zero-velocity curves in the vicinity of the small body is described and feasible motion region is analyzed. The limited condition and the periapsis radius corresponding to different eccentricity against impact surface are presented. The stability of direct and retrograde equator orbits is analyzed based on the perturbation solutions of mean orbit elements.展开更多
In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and fo...In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto(GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective,reliable and does not require any restrictive assumptions for nonlinear terms.展开更多
文摘The orbital dynamics equation of a spacecraft around an irregular sphere small body is established based on the small body’s gravitational potential approximated with a tri-axial ellipsoid. According to the Jacobi integral constant, the spacecraft zero-velocity curves in the vicinity of the small body is described and feasible motion region is analyzed. The limited condition and the periapsis radius corresponding to different eccentricity against impact surface are presented. The stability of direct and retrograde equator orbits is analyzed based on the perturbation solutions of mean orbit elements.
文摘In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto(GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective,reliable and does not require any restrictive assumptions for nonlinear terms.
