The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
Sulla base di una teoria generalizzata di Meccanica Classica per il problema dei Due Corpi, recentemente formulata dall'autore, si considera la questione della precessione del perielio dei pianeti, assente nel caso Newtoniano. Si mostra come la descrizione di questo fenomeno in tale teoria generalizzata è sostanzialmente equivalente a quella offerta dalla Relatività Generale.
Without making recourse to Newton's law of gravitation and starting from the concept of gravitational force, the concepts of active gravitational mass and of passive gravitational mass are introduced. Furthermore it is proved that they can be identified and that in Newton's law of gravitation the linear dependence on masses necessarily follows from the principle of superposition of simultaneous forces and from Newton's third law of dynamics.
Dans un espace linéaire -fois étendu on peut introduire à l’aide de deux fonctions une certaine métrique (les propriétés de ces fonctions étant précisées dans l’article présenté), les courbes géodésiques au sens de centre métrique sont par le système correspondant des équations différentielles d’ordre deux sous les conditions initiales globalement déterminées. Dans le cas et pour une élection simple des fonctions considérées les sourbes géodésiques correspondent aux trajectories d’un point matériel...