Mathematical Discoveries: Celestial Encounters.

Symplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

Celestial mechanics.

Albouy, Alain (Paris, France) Belbruno, Ed (Princeton, USA) Buck, Gregory (Saint Anselm College, USA) Chenciner, Alain (Paris, France) Corbera, Montserrat (Universitat de Vic, Spain) Cushman, Richard (Utrecht, Holland and Calgary, Canada) Diacu, Florin (Victoria, Canada) Gerver, Joseph (Rutgers, USA) Hampton, Marshall (Minneapolis, USA) Kotsireas, Ilias (Wilfried Laurier, Waterloo, Canada) Laco...

The Motion of Celestial Bodies

The history of celestial mechanics is first briefly surveyed, identifying the major contributors and their contributions. The Ptolemaic and Copernican world models, Kepler’s laws of planetary motion and Newton’s laws of universal gravity are presented. It is shown that the orbit of a body moving under the gravitational attraction of another body can be represented by a conic section. The six or...

From the Workshop of Discoveries From the Workshop of Discoveries

Celestial Mechanics of Elastic Bodies

We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.