By Florin Diacu

ISBN-10: 0821891367

ISBN-13: 9780821891360

The writer considers the three -dimensional gravitational n -body challenge, n 2 , in areas of continuous Gaussian curvature okay ' zero , i.e. on spheres S three ?' , for ?>0 , and on hyperbolic manifolds H three ?', for ?<0 . His aim is to outline and learn relative equilibria, that are orbits whose mutual distances stay consistent in time. He additionally in short discusses the difficulty of singularities so as to stay away from very unlikely configurations. He derives the equations of movement and defines six periods of relative equilibria, which stick with clearly from the geometric houses of S three ? and H three ? . Then he proves numerous standards, every one expressing the stipulations for the life of a undeniable category of relative equilibria, a few of that have an easy rotation, while others practice a double rotation, and he describes their qualitative behaviour