# Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems

@inproceedings{Wang2021HamiltonJacobiEO, title={Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems}, author={Hong Yu Wang}, year={2021} }

: 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 de…

## 3 Citations

### Hamilton-Jacobi Equations of Controlled Magnetic Hamiltonian System with Nonholonomic Constraint

- Mathematics
- 2021

. In order to describe the impact of diﬀerent geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we ﬁrst deﬁne a kind of controlled…

### Geometric Reductions, Dynamics and Controls for Hamiltonian System with Symmetry

- Mathematics
- 2022

This is a survey article, from the viewpoint of the completeness of the MarsdenWeinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi…

### Nonholonomic Controlled Hamiltonian System: Symmetric Reduction and Hamilton-Jacobi Equations

- Mathematics
- 2022

: In order to describe the impact of nonholonomic constraints for the dynamics of a regular controlled Hamiltonian (RCH) system, in this paper, for an RCH system with nonholonomic constraint, we ﬁrst…

## References

SHOWING 1-10 OF 35 REFERENCES

### Momentum Maps and Hamiltonian Reduction

- Mathematics
- 2003

Introduction.- Manifolds and smooth structures.- Lie group actions.- Pseudogroups and groupoids.- The standard momentum map.- Generalizations of the momentum map.- Regular symplectic reduction…

### Lectures on Mechanics

- Medicine
- 1993

It's important for you to start having that hobby that will lead you to join in better concept of life and reading will be a positive activity to do every time.

### Introduction to mechanics and symmetry

- Physics
- 1994

Note: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27

### Poisson reduction by controllability distribution for a controlled Hamiltonian system

- arXiv: math/1312.7047, 2013. 38 H. Wang / Commun. Math. Res., x
- 2022

### Lie-Poisson integrators and Lie-Poisson Hamilton-Jacobi theory

- Phys. Lett. A,
- 1988

### Symmetric Reduction and Hamilton-Jacobi Equations of the Controlled Underwater Vehicle-Rotor System

- Mathematics
- 2013

In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the…

### Dynamical Equations of Controlled Rigid Spacecraft with a Rotor

- Mathematics
- 2020

In this paper, we consider the controlled rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and…

### Hamilton-Jacobi Theorems for Regular Reducible Hamiltonian Systems on a Cotangent Bundle

- Mathematics
- 2013

### Hamilton-Jacobi Equations for Nonholonomic Reducible Hamiltonian Systems on a Cotangent Bundle

- Mathematics
- 2015

In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the…