Departmental Papers (ESE)
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.
Document Type
Journal Article
Subject Area
GRASP, Kodlab
Date of this Version
December 2000
Keywords
running, central force, perturbation, approximation, mean value theorem, picard iterates, plant model, return map, hamiltonian mechanics
Date Posted: 30 June 2008
This document has been peer reviewed.
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.