Dynamic Connections in Analytical Mechanics

Gennadi A. Sardanashvily, Luigi Mangiarotti

Publication date: 27 May 1998

Abstract: It is shown that any dynamic equation on a configuration bundle $Q o R$ of non-relativistic time-dependent mechanics is associated with connections on the affine jet bundle $J^1Q o Q$ and on the tangent bundle $TQ o Q$. As a consequence, any non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ o Q$. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied. The geometric notions of reference frames and relative accelerations in non-relativistic mechanics are introduced in the terms of connections. The covariant form of non-relativistic dynamic equations is written.

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