Summary
A certain subset of solutions to the Currie-Hill covariance condition for relativistic classical mechanics of two particles is found to satisfy coupled nonlinear partial differential equations even in the nonrelativistic limit. For this class of forces, the equations of motion are the same whether equal-time or unequal-time surfaces are used, even in the nonrelativistic limit.
Riassunto
Si trova che un certo sottoinsieme di soluzioni della condizione di covarianza di Currie-Hill per la meccanica relativistica classica di due particelle soddisfa equazioni differenziali parziali, non lineari, accoppiate anche nel limite non relativistico. Per questa classe di forze le equazioni del moto souo le stesse sia che si usino superfici di tempo uguale o superfici di tempo disuguale, auche nel limite non relativistico.
Резюме
Получается, что некоторая подсистема решений условия ковариантности Кюри-Хилла для рглятивистской классической механики двух частиц удовлетворяет связанным нелинейным диффзрэнциальным уравненияи в частных производных, даже в нерзлятивистском пределе. Для этого класса сил уравнения движения являются одинаковыми, вне зависимости используются ли равновременные или неравнопре-мгнныг повгрхности, даже в нерелятивистском случае.
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This work was supported in part by Moorhead State College research funds.
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Wray, J.G. On the nonrelativistic limit of action-at-a-distance relativistic classical mechanics. Nuov Cim B 12, 231–238 (1972). https://doi.org/10.1007/BF02822632
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DOI: https://doi.org/10.1007/BF02822632