The Role of Symmetry and Dissipation in Biolocomotion
Abstract
In this paper we illustrate the potential role which relative limit cycles may play in biolocomotion. We do this by describing, in great detail, an elementary example of reduction of a lightly dissipative system modeling crawling-type locomotion in three dimensions. The symmetry group SE(2) is the set of rigid transformations of the horizontal (ground) plane. Given a time-periodic perturbation, the system will admit a relative limit cycle whereupon each period is related to the previous by a fixed translation and rotation along the ground. This toy model identifies how symmetry reduction and dissipation can conspire to create robust behavior in crawling, and possibly walking, locomotion. (An erratum is attached.)
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Published In
SIAM Journal on Applied Dynamical Systems
Pages: 24 - 59
DOI: 10.1137/140970914
ISSN (online): 1536-0040
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© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 29 May 2014
Accepted: 12 November 2015
Published online: 20 January 2016
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