Euler-Poincaré Reduction of a Rigid Body Motion

Rafal Wisniewski, P. Kulczycki

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearch

Abstract

If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems. A control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical system on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well-known Euler-Poincaré reduction to a rigid body motion with forcing.
Original languageDanish
Title of host publicationProceedings of the 10th IEEE International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Polen
Publication date2004
Pages813-818
Publication statusPublished - 2004
EventEuler-Poincaré Reduction of a Rigid Body Motion -
Duration: 30 Aug 2004 → …

Conference

ConferenceEuler-Poincaré Reduction of a Rigid Body Motion
Period30/08/2004 → …

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