Symplectic Geometric Methods for Matrix Differential Equations Arising from Inertial Navigation Problems
This work addresses inertial navigation problems, offering incremental improvements by applying existing methods to new system dimensions.
The paper tackles matrix differential equations from inertial navigation by analyzing their symplectic and orthogonal properties, extending symplectic geometric algorithms to odd-dimensional systems, and validating results through numerical experiments.
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.