Departmental Papers (ESE)

Document Type

Journal Article

Subject Area


Date of this Version

December 2000


Postprint version. Published in Journal of Nonlinear Science, Volume 10, Issue 5, December 2000, pages 533-568.
Publisher URL:

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.


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.


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.