Published June 1, 1995
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Technical Report
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The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint
- Creators
- Lewis, Andrew D.
Chicago
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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.
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.Files
CDS95-014.pdf
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Additional details
- Eprint ID
- 28095
- Resolver ID
- CaltechCDSTR:1995.014
- Created
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2006-10-10Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Caltech groups
- Control and Dynamical Systems Technical Reports