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Most General Form of the Lagrange Function for Classical Two Particle Equation of Motion Covariant under Galilei Transformation in (1 + 1) and (3 + 1) Dimensional Spaces
Author(s) -
Łopuszański J.,
Stichel P. C.
Publication year - 1997
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190450105
Subject(s) - covariant transformation , equations of motion , invariant (physics) , mathematics , transformation (genetics) , classical mechanics , motion (physics) , mathematical physics , physics , mathematical analysis , biochemistry , chemistry , gene
In the present note we give the most general form of a non‐relativistic Lagrange function for two point particles moving according to some classical equations of motion. We do not specify the form of these equations. We require only that these equations should be form invariant with respect to the Galilei transformations and should be derivable from a Lagrange function as its Euler‐Lagrange Equations. We present also some of the generators of the Galilei group and their Lie‐Cartan commutation relations.