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The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint

Lewis, Andrew D. (1995) The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1995.014

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Abstract

We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell equations is shown to be valid in the case when constraints and external forces are present. In the case when the Lagrangian is the kinetic energy with respect to a Riemannian metric, the Gibbs function is shown to be related to the kinetic energy on the tangent bundle of the configuration manifold with respect to the Sasaki metric. We also make a connection with the Gibbs-Appell equations and Gauss' principle of least constraint in the general case.


Item Type:Report or Paper (Technical Report)
Additional Information:The author would like to thank Gabor Stepan for his introduction to the Gibbs-Appell equations. Discussions with Richard Murray and Jim Ostrowski have also been helpful. Jerry Marsden pointed out the link with the Sasaki metric discussed in Section 6. Submitted to Reports on Mathematical Physics.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1995.014
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1995.014
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28095
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:10 Oct 2006
Last Modified:26 Dec 2012 14:30

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