Premium
The Most General Set of Lagrange Functions Yielding Galilei Covariant Equations of Motion Having the Same Set of Solutions
Author(s) -
Cislo J.,
Łopuszanski J.,
Stichel P.C.
Publication year - 1998
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(199802)46:1<45::aid-prop45>3.0.co;2-0
Subject(s) - covariant transformation , mathematics , constraint algorithm , formalism (music) , equations of motion , motion (physics) , mathematical analysis , lagrange multiplier , classical mechanics , physics , mathematical physics , mathematical optimization , art , musical , visual arts
The nonrelativistic case of two point particles in the (1 + 1)‐dimensional space is considered. The existence of an autonomous Lagrange function is assumed, whose Euler‐Lagrange Equations are forminvariant under the Galilei group. We show how to find all autonomous Lagrange functions, giving rise to Euler‐Lagrange Eqzations, which again are Galilei covariant and whose set of solutions coincides with the set of solutions of the original equations, we started with. We are going to construct explicitly the most general expressions for the Lagrange functions as well as for the Equations of Motion. We supplement our considerations by some simple examples. We give also a short account on an extension of our formalism to the case of Equations of Motion, which are no longer Galilei covariant but whose solutions belong still to the same set as the previous one.