Departmental Papers (ESE)


Examination of total energy shows that the global limit behavior of a dissipative mechanical system is essentially equivalent to that of its constituent gradient vector field. The class of “navigation functions” is introduced and shown to result in “almost global” asymptotic stability for closed loop mechanical control systems upon which a navigation function has been imposed as an artifical potential energy. Two examples from the engineering literature - satellite attitude tracking and robot obstacle avoidance - are provided to demonstrate the utility of these observations.

For more information: Kod*Lab

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version


Publication Source

Contemporary Mathematics



Start Page


Last Page



Preprint version. First published in Control Theory and Multibody Systems , in Volume 97, 1989, pages 131-158, published by the American Mathematical Society in the Contemporary Mathematics series.

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

Bib Tex

@article{koditschek-contemporary mathematics-1989, author = {Daniel E. Koditschek}, title = {The Application of Total Energy as a Lyapunov Function for Mechanical Control Systems}, booktitle = {Contemporary Mathematics}, year = {1989}, month = {February}, }



Date Posted: 25 July 2014

This document has been peer reviewed.