Research On Iterative Pseudospectral Method Solving Astrodynamics Problem

With the development of space science and technology, astrodynamics as a key concern in space domain have been done a deep research on both home and broad. The paper Hamiltonian modeling the orbit motion and relative motion of spacecraft based on the Hamilton theory, and applications of the iterative pseudospectral procedure solved these models.The main contents and accomplishments are as follows:The Hamilton system and Hamilton's canonical equation based on analysis mechanics keystone are introduced, and Hamilton modeling the orbit motion of spacecraft incorporate all conservative perturbations,two-point boundary-value problems of this model namely the perturbed Lambert's problem.we had Hamiltonian modeling the relative motion of spacecrafts incorporate all conservative perturbations,and this model is the bedrock for Hamiltonian modeling the relative motion control of spacecraft.The pseudospectral method and iterative solving procedure for the differential equation are introduced.There are Fourier and Legendre and Chebyshev pseudospectral method with different interpolating polynomials,these methods are all base on Lagrange interpolating theory. The Chebyshev pseudospectral method is emphasized in these methods, and iterative solving the nonlinear differential equations with the Chebyshev method.This paper utilizes the iterative pseudospectral method solving the Hamilton modeling relative motion of spacecraft. aim at relative motion of formation flying spacecraft, and introduced the full iterative solving procedure for the relative motion of formation flying spacecraft. Sovled the circular and ellipse reference orbit incorporate all conservative perturbations, whatever initial value or two-point boundary-value problems, it can obtain a high precision result, and validated the iterative pseudospectral method solving astrodynamics availably.Iterative pseudospectral method solving the Hamilton modeling optimal control of Formation Flying Spacecraft relative motion is introduced. Characterized the optimal control's problem and optimization simply, Hamilton modeling optimal control of formation flying spacecraft relative motion based on Hamilton modeling relative motion of spacecraft, described Chebyshev pseudospectral method solving the optimal control of formation flying spacecraft relative motion with extremum theory and full iterative solving procedure. Sovling the circular and ellipse reference orbit incorporate all conservative perturbations of the optimal control of formation flying spacecraft relative motion, the result indicates the iterative pseudospectral method can obtain a high control precision. Describing the Lambert's problem simply and utilizing the iterative pseudospectral method solving the perturbed Lambert's problem.Solving Lambert's problem with improving Guass'method, Taking the solution to Lambert's problem as the nominal solution, the iterative pseudospectral method provides an efficient way to solve the perturbed Lambert's problem. Utilized perturbed Hohmann transfer orbit and general transfer orbit examples validated this method solving the perturbed Lambert's problem availably.