TY - JOUR
T1 - Hamilton-Jacobi Equations for Nonholonomic Magnetic Hamiltonian Systems
AU - Wang , Hong
JO - Communications in Mathematical Research 
VL - 3
SP - 351
EP - 388
PY - 2022
DA - 2022/08
SN - 38
DO - http://doi.org/10.4208/cmr.2022-0028
UR - https://global-sci.org/intro/article_detail/cmr/20961.html
KW - Hamilton-Jacobi equation, magnetic Hamiltonian system, nonholonomic constraint, distributional magnetic Hamiltonian system, nonholonomic reduction.
AB - <p style="text-align: justify;">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.</p>