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Published September 15, 2010 | Updated
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Remarks on Geometric Mechanics


This paper gives a few new developments in mechanics, as well as some remarks of a historical nature. To keep the discussion focused, most of the paper is confined to equations of "rigid body", or "hydrodynamic" type on Lie algebras or their duals. In particular, we will develop the variational structure of these equations and will relate it to the standard variational principle of Hamilton.

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October, 1992, this version: March 22, 1996. "This book, was written to celebrate the 50th anniversary of the Mathematical Research Institute at Oberwolfach" I would like to especially thank Hans Duistermaat, Tudor Ratiu, Jürgen Scheurle, Juan Simo, Alan Weinstein, and Norman Wildberger for helpful discussions and comments. Sections 3 and 4 are based on notes kindly supplied by Hans Duistermaat and are gratefully acknowledged. Some of the original research reported here was done jointly with Jürgen Scheurle, and is hereby acknowledged as well.

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August 20, 2023
August 20, 2023