Departmental Papers (ESE)

Document Type

Journal Article

Date of this Version

December 2000

Comments

Postprint version. Published in Journal of Nonlinear Science, Volume 10, Issue 5, December 2000, pages 533-568.
Publisher URL: http://dx.doi.org/10.1007/s004530010001

NOTE: At the time of publication, author Daniel Koditschek was affiliated with the University of Michigan. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.

Abstract

We report in this paper a relatively simple means of generating closed-form approximants to the return map associated with a family of nonintegrable Hamiltonian systems. These systems arise in consideration of legged locomotion by animals and robots. The approximations proceed through the iterated application of the mean value theorem for integral operators applied to a nonintegrable perturbation of the system of interest. Both the accuracy of these approximants and their algebraic intractability grow in a relatively controlled manner.

Keywords

running, central force, perturbation, approximation, mean value theorem, picard iterates, plant model, return map, hamiltonian mechanics

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Date Posted: 30 June 2008

This document has been peer reviewed.