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Relativistic and Non-relativistic Equations of Motion

L. Mangiarotti·G. Sardanashvily
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Abstract

It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.

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L. Mangiarotti, G. Sardanashvily. 1998-05-21. Relativistic and Non-relativistic Equations of Motion. https://arxiv.org/abs/gr-qc/9805081

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