Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2112.00961,
title = {Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems},
author = {Hong Wang},
journal= {arXiv preprint arXiv:2112.00961},
year = {2022}
}
Comments
27 pages. arXiv admin note: substantial text overlap with arXiv:2110.14175, arXiv:1508.07548