IKBFU's Vestnik

2009 Issue №04

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The conservation laws in the Euler problem about two attractive centers and the integration of the dynamic equations

DOI
10.5922/2223-2095-2009-4-1
Pages
8-11

Abstract

The article establishes that Euler’s problem of two attractive centres contains another conservation law alongside with the energy conservation
one, which is also quadratic in velocities. These conservation laws and elliptic coordinates considerably simplify the procedure of trajectory equations generation.

Reference

1. Euler L. Probleme. Un corps ètant attirè en raison rèciproque quarrèe des distances vers deux points fixes donnès, trouver les cas où la courbe dècrite par ce corps sera algèbrique //Histoire de L’Acadèmie Royale des sciences et Belles-lettres. (1760), 1767. V. XVI. P. 228—249. 2. Euler L. De motu corporis ad duo centra virium fixa attracti //Novi Commentarii Acade¬miae Scientiarum Imperialis Petropolitanae. (1764), 1766. V. X. P. 207—242. 3. Герасимов И. А. Задача двух неподвижных центров Л. Эйлера. Фря¬зино, 2007.