Dynamics and control of a 3D pendulum

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

Research output: Contribution to journalConference article

79 Citations (Scopus)

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 languageEnglish (US)
Article numberTuA09.6
Pages (from-to)323-328
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume1
StatePublished - Dec 1 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

Fingerprint

Pendulum
Pendulums
Pivot
Rigid Body
Model
Force Control
Force control
Nonlinear Control
Barycentre
Nonlinear Dynamics
Control Problem
Degree of freedom
Moment
Distinct
Symmetry

ASJC Scopus subject areas

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

Cite this

Shen, J., Sanyal, A., Chaturvedi, N. A., Bernstein, D., & McClamroch, H. (2004). Dynamics and control of a 3D pendulum. 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.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 1, TuA09.6, 01.12.2004, p. 323-328.

Research output: Contribution to journalConference article

Shen, J, Sanyal, A, Chaturvedi, NA, Bernstein, D & McClamroch, H 2004, 'Dynamics and control of a 3D pendulum', Proceedings of the IEEE Conference on Decision and Control, vol. 1, TuA09.6, pp. 323-328.
Shen J, Sanyal A, Chaturvedi NA, Bernstein D, McClamroch H. Dynamics and control of a 3D pendulum. Proceedings of the IEEE Conference on Decision and Control. 2004 Dec 1;1:323-328. TuA09.6.
Shen, Jinglai ; Sanyal, Amit ; Chaturvedi, Nalin A. ; Bernstein, Dennis ; McClamroch, Harris. / Dynamics and control of a 3D pendulum. In: Proceedings of the IEEE Conference on Decision and Control. 2004 ; Vol. 1. pp. 323-328.
@article{b317280eab6f4608a38c7d954fcd02c6,
title = "Dynamics and control of a 3D pendulum",
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.",
author = "Jinglai Shen and Amit Sanyal and Chaturvedi, {Nalin A.} and Dennis Bernstein and Harris McClamroch",
year = "2004",
month = "12",
day = "1",
language = "English (US)",
volume = "1",
pages = "323--328",
journal = "Proceedings of the IEEE Conference on Decision and Control",
issn = "0191-2216",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

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 -