具有非完整约束的接触哈密顿系统和拉格朗日系统

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI:10.3934/jgm.2021001

M. León, V. M. Jiménez, M. Lainz

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引用次数: 15

摘要

在本文中，我们发展了具有非完整约束的接触系统理论。通过对变量进行限制，使其满足非完整约束，利用赫格罗茨变分原理得到动力学。证明了非完整动力学可以用无约束哈密顿向量场的投影来表示。最后构造了非完整支架，它是可观测空间上的几乎雅可比支架，并给出了该支架的非完整动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Contact Hamiltonian and Lagrangian systems with nonholonomic constraints

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.