A Caltech Library Service

The energy–momentum method for the stability of non-holonomic systems

Zenkov, Dmitry V. and Bloch, Anthony M. and Marsden, Jerrold E. (1998) The energy–momentum method for the stability of non-holonomic systems. Dynamics and Stability of Systems, 13 (2). pp. 123-166. ISSN 1465-3389.

PDF - Updated Version
See Usage Policy.


Use this Persistent URL to link to this item:


In this paper we analyze the stability of relative equilibria of nonholonomic systems (that is, mechanical systems with nonintegrable constraints such as rolling constraints). In the absence of external dissipation, such systems conserve energy, but nonetheless can exhibit both neutrally stable and asymptotically stable, as well as linearly unstable relative equilibria. To carry out the stability analysis, we use a generalization of the energy-momentum method combined with the Lyapunov-Malkin theorem and the center manifold theorem. While this approach is consistent with the energy-momentum method for holonomic systems, it extends it in substantial ways. The theory is illustrated with several examples, including the the rolling disk, the roller racer, and the rattleback top.

Item Type:Article
Related URLs:
Additional Information:© 1998, Taylor & Francis. this version: June 19, 1998. Research partially supported by National Science Foundation PYI grant DMS–94–96221 and AFOSR grant F49620-96-1-0100 Research partially supported by National Science Foundation PYI grant DMS–94–96221, AFOSR grant F49620-96-1-0100, a Guggenheim Fellowship and the Institute for Advanced Study Research partially supported by the National Science Foundation. We would like to thank J. Burdick, P. Crouch, W. Koon, P. Krishnaprasad, and R. Murray for helpful comments and suggestions.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0100
Guggenheim FellowshipUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Classification Code:AMS Subject Classification: 70H05, 53C22
Record Number:CaltechAUTHORS:20100923-085233667
Persistent URL:
Official Citation:The energy-momentum method for the stability of non-holonomic systems Authors: Dmitry V. Zenkov; Anthony M. Bloch; Jerrold E. Marsden
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20094
Deposited By: Ruth Sustaita
Deposited On:24 Sep 2010 21:07
Last Modified:26 Dec 2012 12:27

Repository Staff Only: item control page