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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
William J. Schwind and Daniel E. Koditschek, "Approximating the Stance Map of a 2 DOF Monoped Runner", . December 2000.
Date Posted: 30 June 2008
This document has been peer reviewed.