Vol. 2, No. 8, 2007

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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
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