Euler-Poincaré Reduction of Externally Forced Rigid Body Motion

Rafal Wisniewski, P. Kulczycki

Publikation: Bidrag til tidsskriftTidsskriftartikelFormidling

Resumé

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.
OriginalsprogDansk
TidsskriftControl and Cybernetics
Vol/bind33
Udgave nummer2
Sider (fra-til)297-310
ISSN0324-8569
StatusUdgivet - 2004

Citer dette

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Euler-Poincaré Reduction of Externally Forced Rigid Body Motion. / Wisniewski, Rafal; Kulczycki, P.

I: Control and Cybernetics, Bind 33, Nr. 2, 2004, s. 297-310.

Publikation: Bidrag til tidsskriftTidsskriftartikelFormidling

TY - JOUR

T1 - Euler-Poincaré Reduction of Externally Forced Rigid Body Motion

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AU - Kulczycki, P.

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N2 - 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.

AB - 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.

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