In mechanics, it has been accepted since the time of Lagrange (1788) that the physical motion of systems of rigid bodies obeys a variational principle wherein energy is minimised. This principle has been reexamined and found to generally not hold by Hertz in 1894. Since the early 1990’s, this seeming paradox has been examined by many researchers and some understanding exists of when variational principles describe physical motion. In this work, the issue is cast in a geometric setting which enables a comprehensive understanding of the rôle of variational principles in mechanics.

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