Symplectic Geometric Methods for Matrix Differential Equations Arising from Inertial Navigation Problems

Abstract: This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality. Furthermore, it extends the applicable fields of symplectic geometric algorithms from the even dimensional Hamiltonian system to the odd dimensional dynamical system. Finally, some numerical experiments are presented and illustrate the theoretical results of this paper.