Advanced Mechanics. Mathematical Introduction

Giovanni Giachetta, G. Sardanashvily, L. Mangiarotti

Publication date: 3 November 2009

Abstract: 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.

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