1998/05/27 by L. Mangiarotti, Mangiarotti, L., G. Sardanashvily +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #Geophysics and Sensor Technology #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/9805024
21 pages, LaTeX
arxiv created 1998/05/27 · openalex publication_date 1998/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that any dynamic equation on a configuration bundle Q→ R of non-relativistic time-dependent mechanics is associated with connections on the affine jet bundle J1Q→ Q and on the tangent bundle TQ→ 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→ 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.