2021/12/02 by Hong Wang, Wang, Hong
Engineering · Mathematics · Physics and Astronomy · #53D20 #70F25 #70H20 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2112.00961
openalex publication_date 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to describe the impact of different geometric structures and constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we first drive precisely the geometric constraint conditions of magnetic symplectic form for the magnetic Hamiltonian vector field.which are called the Type I and Type II of Hamilton-Jacobi equation. Secondly, for the magnetic Hamiltonian system with nonholonomic constraint, we first define a distributional magnetic Hamiltonian system, then derive its two types of Hamilton-Jacobi equation. Moreover, we generalize the above results to nonholonomic reducible magnetic Hamiltonian system with symmetry. We define a nonholonomic reduced distributional magnetic Hamiltonian system, and prove two types of Hamilton-Jacobi theorem. These research work reveal the deeply internal relationships of the magnetic symplectic structure, nonholonomic constraint, the distributional two-form, and the dynamical vector field of the nonholonomic magnetic Hamiltonian system.