Dynamics and control of a 3D pendulum

Jinglai Shen, Amit K. Sanyal, Nalin A. Chaturvedi, Dennis Bernstein, Harris McClamroch

Research output: Contribution to journalConference Articlepeer-review

103 Scopus citations


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 ID 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.

Original languageEnglish (US)
Article numberTuA09.6
Pages (from-to)323-328
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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