On invariant manifolds of nonholonomic systems

被引：0

作者：

Valery V. Kozlov

机构：

[1] Russian Academy of Sciences,V.A. Steklov Mathematical Institute

来源：

Regular and Chaotic Dynamics | 2012年 / 17卷

关键词：

invariant manifold; Lamb’s equation; vortex manifold; Bernoulli’s theorem; Helmholtz’ theorem; 70Hxx; 37J60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamiltonian systems. As an illustration, nonholonomic systems on Lie groups with a left-invariant metric and left-invariant (right-invariant) constraints are considered.

引用

页码：131 / 141

页数：10

共 9 条

[1] Kozlov V.V.(1983)Notes on Steady Vortex Motions of Continuous Medium Prikl. Mat. Mekh. 47 341-342
[2] Arnold V. I.(1993)Mathematical Aspects of Classical and Celestial Mechanics Encyclopaedia Math. Sci. 3 1-291
[3] Kozlov V.V.(1987)On the Existence of an Integral Invariant of a Smooth Dynamic System Prikl. Mat. Mekh. 51 538-545
[4] Neishtadt A. I.(1986)Flows on Lie Groups with a Nonholonomic Constraint and Integrable Non-Hamiltonian Systems Funktsional. Anal. i Prilozhen. 20 65-66
[5] Kozlov V.V.(1978)On Theorems of Dynamics Prikl. Mat. Mekh. 42 28-33
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