### Abstract

Original language | Danish |
---|---|

Journal | Control and Cybernetics |

Volume | 33 |

Issue number | 2 |

Pages (from-to) | 297-310 |

ISSN | 0324-8569 |

Publication status | Published - 2004 |

### Cite this

*Control and Cybernetics*,

*33*(2), 297-310.

}

*Control and Cybernetics*, vol. 33, no. 2, pp. 297-310.

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

Research output: Contribution to journal › Journal article › Communication

TY - JOUR

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

AU - Wisniewski, Rafal

AU - Kulczycki, P.

PY - 2004

Y1 - 2004

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.

M3 - Tidsskriftartikel

VL - 33

SP - 297

EP - 310

JO - Control and Cybernetics

JF - Control and Cybernetics

SN - 0324-8569

IS - 2

ER -