HamiltonJacobi 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 HamiltonJacobi equation. Secondly, for the magnetic Hamiltonian system with nonholonomic constraint, we first define a distributional magnetic Hamiltonian system, then derive its two types of HamiltonJacobi 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 HamiltonJacobi theorem. These research work reveal the deeply internal relationships of the magnetic symplectic structure, nonholonomic constraint, the distributional twoform, and the dynamical vector field of the nonholonomic magnetic Hamiltonian system.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.00961
 Bibcode:
 2021arXiv211200961W
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 53D20;
 70H20;
 70F25
 EPrint:
 27 pages. arXiv admin note: substantial text overlap with arXiv:2110.14175, arXiv:1508.07548