Hamilton–Pontryagin spectral-collocation methods for the orbit propagation

作     者：Zhonggui Yi Baozeng Yue Mingle Deng 

作者机构：School of Aerospace EngineeringBeijing Institute of TechnologyBeijing100081China China Academy of Space TechnologyBeijing100094China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2021年第37卷第11期

页      面：1696-1713,I0003页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grants 11772049 and 12132002) 

主　　题：Hamilton-Pontryagin principle Spectral-collocation method Lie groups Variational integrator Orbit propagation 

摘      要：According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanical systems by employing the spectral-collocation method to discretize the corresponding Lagrangian and kinematic *** constructed framework can be transformed easily to the well-known symplectic partitioned Runge–Kutta methods and the higher order symplectic partitioned Lie Group methods by choosing same interpolation nodes and quadrature *** numerical experiments about the orbit propagation of Kepler two-body system and the rigid-body flow propagation of a free rigid body are conducted,*** simulating results reveal that the constructed update schemes can possess simultaneously the excellent exponent convergence rates of spectral methods and the attractive long-term structure-preserving properties of geometric numerical algorithms.