Straight and circular motions of a particle in the field of two fixed attractors. (English) Zbl 1241.70021

Scarpello, Giovanni Mingari; Palestini, Arsen; Ritelli, Daniele

J. Geom. Symmetry Phys. 11, 49-66 (2008).

Summary: The two centre problem is studied both in the phase plane and in spacetime, assuming first a trajectory collinear, and, as a second case, a circular one through the Newtonian attractors, finding a saddle equilibrium. For the latter problem, a probably new differential equation is met and solved. Time is then obtained in both cases through elliptic integrals of all kinds and Jacobian functions.

MSC:

70F99

Dynamics of a system of particles, including celestial mechanics

Keywords:

phase plane; saddle equilibrium; elliptic integrals; Jacobian functions