2009/11/03 by Giachetta, G., Mangiarotti, L., Sardanashvily, G.
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.0911.0411
Classical non-relativistic mechanics in a general setting of time-dependent transformations and reference frame changes is formulated in the terms of fibre bundles over the time-axis R. Connections on fibre bundles are the main ingredient in this formulation of mechanics which thus is covariant under reference frame transformations. The basic notions of a non-relativistic reference frame, a relative velocity, a free motion equation, a relative acceleration, an external force are formulated. Newtonian, Lagrangian, Hamiltonian mechanical systems and the relations between them are defined. Lagrangian and Hamiltonian conservation laws are considered.