Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
- 12 October 2008
- journal article
- review article
- Published by Pleiades Publishing Ltd in Regular and Chaotic Dynamics
- Vol. 13 (5) , 443-490
Abstract
This paper can be regarded as a continuation of our previous work [1, 2] on the hierarchy of the dynamical behavior of nonholonomic systems. We consider different mechanical systems with nonholonomic constraints; in particular, we examine the existence of tensor invariants (laws of conservation) and their connection with the behavior of a system. Considerable attention is given to the possibility of conformally Hamiltonian representation of the equations of motion, which is mainly used for the integration of the considered systems.Keywords
This publication has 53 references indexed in Scilit:
- Geometric representation of detachment conditions in systems with unilateral constraintRegular and Chaotic Dynamics, 2008
- On the theory of motion of nonholonomic systems. The reducing-multiplier theoremRegular and Chaotic Dynamics, 2008
- On detachment conditions in the problem on the motion of a rigid body on a rough planeRegular and Chaotic Dynamics, 2008
- Rolling balls and octonionsProceedings of the Steklov Institute of Mathematics, 2007
- Reduction of almost Poisson brackets for nonholonomic systems on Lie groupsRegular and Chaotic Dynamics, 2007
- Rolling of a non-homogeneous ball over a sphere without slipping and twistingRegular and Chaotic Dynamics, 2007
- Rubber rolling over a sphereRegular and Chaotic Dynamics, 2007
- Obstacle to the reduction of nonholonomic systems to the Hamiltonian formDoklady Physics, 2002
- Integrable nonholonomic systems on Lie groupsMathematical Notes, 1988
- Ueber die Bewegung eines festen Körpers in einer Flüssigkeit.Journal für die reine und angewandte Mathematik (Crelles Journal), 1892