Year: 2022
Author: Hong Wang
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 351–388
Abstract
In order to describe the impact of the different geometric structures and the constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we drive precisely the geometric constraint conditions of the magnetic symplectic form for the magnetic Hamiltonian vector field, which are called the Type I and Type II Hamilton-Jacobi equations. Second, for the magnetic Hamiltonian system with a nonholonomic constraint, we can define a distributional magnetic Hamiltonian system, then derive its two types of Hamilton-Jacobi equations. 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 the two types of Hamilton-Jacobi theorems. These research reveal the deeply internal relationships of the magnetic symplectic structure, the nonholonomic constraint, the distributional two-form, and the dynamical vector field of the nonholonomic magnetic Hamiltonian system.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0028
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 351–388
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Hamilton-Jacobi equation magnetic Hamiltonian system nonholonomic constraint distributional magnetic Hamiltonian system nonholonomic reduction.
Author Details
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Hamilton-Jacobi Equations for a Regular Controlled Hamiltonian System and its Reduced Systems
Wang, Hong
Acta Mathematica Scientia, Vol. 43 (2023), Iss. 2 P.855
https://doi.org/10.1007/s10473-023-0221-5 [Citations: 1]