Dynamics and control of a 3D pendulum
Jinglai Shen
Sanyal, A.K.
Chaturvedi, N.A.
Bernstein, D.
McClamroch, H.
Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA;
This paper appears in: Decision and Control, 2004. CDC. 43rd IEEE Conference on
Publication Date: 14-17 Dec. 2004
Volume: 1,
On page(s): 323- 328 Vol.1
ISSN: 0191-2216
ISBN: 0-7803-8682-5
INSPEC Accession Number: 8381862
Current Version Published: 2005-05-16
Abstract
New pendulum models are introduced and studied. The pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force and control forces and moments. Several different pendulum models are developed to analyze properties of the uncontrolled pendulum. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Rigid pendulum and multi-body pendulum control problems are proposed. The 3D pendulum models provide a rich source of examples for nonlinear dynamics and control, some of which are similar to simpler pendulum models and some of which are completely new.
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