### 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 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 language | English (US) |
---|---|

Article number | TuA09.6 |

Pages (from-to) | 323-328 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 1 |

State | Published - Dec 1 2004 |

Externally published | Yes |

Event | 2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: Dec 14 2004 → Dec 17 2004 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*1*, 323-328. [TuA09.6].

**Dynamics and control of a 3D pendulum.** / Shen, Jinglai; Sanyal, Amit; Chaturvedi, Nalin A.; Bernstein, Dennis; McClamroch, Harris.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 1, TuA09.6, pp. 323-328.

}

TY - JOUR

T1 - Dynamics and control of a 3D pendulum

AU - Shen, Jinglai

AU - Sanyal, Amit

AU - Chaturvedi, Nalin A.

AU - Bernstein, Dennis

AU - McClamroch, Harris

PY - 2004/12/1

Y1 - 2004/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=14344261807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14344261807&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:14344261807

VL - 1

SP - 323

EP - 328

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

M1 - TuA09.6

ER -