Regular and Chaotic Dynamics

, Volume 20, Issue 4, pp 401–427 | Cite as

The dynamics of systems with servoconstraints. II

Article

Abstract

This paper addresses the dynamics of systems with servoconstraints where the constraints are realized by controlling the inertial properties of the system. Vakonomic systems are a particular case. Special attention is given to the motion on Lie groups with left-invariant kinetic energy and a left-invariant constraint. The presence of symmetries allows the dynamical equations to be reduced to a closed system of differential equations with quadratic right-hand sides. As the main example, we consider the rotation of a rigid body with a left-invariant servo-constraint, which implies that the projection of the body’s angular velocity on some body-fixed direction is zero.

Keywords

servoconstraints symmetries Lie groups left-invariant constraints systems with quadratic right-hand sides vakonomic systems 

MSC2010 numbers

70E18 34C40 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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