Vol.3, No 12, 2002 pp. 309-325
UDC 531.011

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RELATIVE MOTION OF SYSTEMS
IN A PARAMETRIC FORMULATION OF MECHANICS
Đorđe Mušicki
Faculty of Physics, University of Belgrade, and Mathematical Institute
Serbian Academy of Sciences and Arts, Belgrade, Yugoslavia

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A parametric formulation of mechanics, formulated by the author himself, is based on the separation of the double role of time by the aid of a family of varied paths, so that the time as independent variable remains unchanged, while it as a parameter is transformed into a new parameter, which depends on a chosen path and is taken as an additional generalized coordinate.
In this paper this parametric formulation of mechanics has been extended to the relative motion of arbitrary rheonomic systems. In this way, the corresponding Lagrangian and Hamiltonian equations, as well as the energy change law for such systems have been formulated and analised, and the obtained results are illustrated by a simple example.

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RELATIVNO KRETANJE SISTEMA
U PARAMETARSKOJ FORMULACIJI MEHANIKE Parametarska formulacija mehanike, formulisana od samog autora, zasniva se na razdvajanju dvostruke uloge vremena za reonomne sisteme (nezavisno promenljiva i parametar) pomoću izvesne familije variranih putanja. Pri tome vreme kao nezavisna promenljiva ostaje nepromenjeno, dok se umesto vremena kao parametra uvodi novi parametar, koji zavisi od izabrane putanje iz ove familije i uzima se kao dopunska generalisana koordinata.
U ovom radu ova parametarska formulacija mehanike proširena je na relativno kretanje proizvoljnih reonomnih sistema. Na taj način, formulisani su i analizirani odgovarajući prošireni sistemi Lagrange-ovih i Hamilton-ovih jednačina, kao i opšti zakon promene energije za ovakve sisteme, a dobijeni rezultati su ilustrovani jednim prostim primerom.