The geometry of the Gibbs-Appell equations and Gauss's Principle of Least Constraint
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Authors
Lewis, Andrew D.
Date
1995
Type
Language
en_US
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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's principle of least constraint in the
general case.
Description
Citation
Reports on Mathematical Physics 38(1), pages 11-28,
1996