×

Solution of the question 2478. (English) JFM 01.0113.02

Educ. Times. IX. 24 u. 25 (1868).
Direkte Herleitung von \[ f+x\left(\frac{\mu}{r}-\frac{dy^{2}+dx^{2}}{dt^{2}}\right)+\frac{ydy+zdz}{dt}\cdot\frac{dx}{dt}=0,\quad f'x\quad \text{etc.} \] aus den 3 Gleichungen: \[ \frac{d^{2}x}{dt^{2}}+\frac{\mu x}{r^{3}}=0,\quad \frac{d^{2}y}{dt^{2}}+\frac{\mu y}{r^{3}}=0,\quad \frac{d^{2}z}{dt^{2}}+\frac{\mu z}{r^{3}}=0, \] siehe Laplace, Méc. cél. II. Cap. III. § 18.

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems