Geometric analysis of the dynamics of a double pendulum

Awrejcewicz, Jan; Sendkowski, Dariusz

doi:10.2140/jomms.2007.2.1421

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Geometric analysis of the dynamics of a double pendulum

Jan Awrejcewicz and Dariusz Sendkowski

Vol. 2 (2007), No. 8, 1421–1430

DOI: 10.2140/jomms.2007.2.1421

Abstract

In this paper we make use of Riemannian geometry to analyze the dynamics of a simple low dimensional system with constraints, namely a double physical pendulum. The dynamics are analyzed by means of the Jacobi–Levi–Civita equation and its solutions. We show that this geometrical approach is in qualitative agreement with the classical techniques devoted to the study of dynamical systems.

Keywords

pendulum, chaos, Riemannian geometry

Milestones

Received: 7 July 2006

Accepted: 20 April 2007

Published: 1 October 2007

Authors

Jan Awrejcewicz
Technical University of Łódź Department of Automatics and Biomechanics Stefanowskiego St. 1/15 Łódź, 90-924 Poland

Dariusz Sendkowski
Technical University of Łódź Department of Automatics and Biomechanics Stefanowskiego St. 1/15 Łódź, 90-924 Poland

Vol. 2, No. 8, 2007

Jan Awrejcewicz and Dariusz Sendkowski

Abstract

Keywords

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Authors