De motu perturbationibusque planetarum secundum legem electrodynamicam Weberianam solem ambientium

Description

Seegers solves Weber's 2-body problem using Jacobi's elliptic functions.

cf. this paper on solving the Weber 2-body problem using perturbation methods (courtesy Assis):

• Tisserand, François Félix. “Sur le mouvement des planètes autour du Soleil, d’après la loi électrodynamique de Weber.” Edited by Joseph Louis François Betrand. Bulletin astronomique 7 (1890).

Duhem also has a § of Bertrand's derivation (cf. p. 166) of Ampère's law in Duhem's Leçons vol. 3 pp. 309-332 (DjVu pp. 322-345).

Re: Tisserand and Bertrand, cf. Jaki's Uneasy Genius p. 152, which quotes Duhem (my emphases):

Twice I was solicited by various persons to present my candidacy, namely, when the death of Tisserand and then the death of J. Bertrand led respectively to a vacancy of the chair of physical mechanics at the Sorbonne and of the chair of mathematical physics at the Collège de France.

Thus, Tisserand and Bertrand seemed to be quite the experts re: mathematical physics at the time.

For a good overview of Weber's law applied to gravity, incl. Seegers's thesis, see Tisserand's Traité de mécanique céleste vol. 4, "Vitesse de propagation de l'attraction," ch. XXVIII (pp. 494-511 // PDF pp. 510-527). Subsection 225 is entitled "Loi d'attraction conforme à la loi électrodynamique de Weber ". He mentions Seegers, discusses how to integrate Weber's force law, and discusses Riemann's and Clausius's laws.

Also cites Jacobi's Vorlesungen über Dynamik.