The implications of Galilean invariance for classical point particle lagrangians

Details The implications of Galilean invariance for classical point particle lagrangians The implications of Galilean invariance for classical point particle lagrangians

2011-12-29

arxiv.org/abs/1112.6318v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

We explore the implications of the requirement of Galilean invariance for classical point particle lagrangians, in which the space is not assumed to be flat to begin with. We show that for the free, time-independent lagrangian, this requirement is equivalent to the existence of gradient Killing vectors on space, which is in turn equivalent to the condition that the space is a direct product, which is totally flat in the Galilean invariant direction. We then consider more general cases and see that there is no simple generalisation to these cases.

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