University Avenue West 75, Waterloo, Ontario, N2L 3C5 Canada
Department of Mathematics, Wilfrid Laurier University
Hu S., Leandro E., Santoprete M.
On the Topology of the Double Spherical Pendulum
2012, vol. 17, no. 1, pp. 36-53
This paper studies the topology of the constant energy surfaces of the double spherical pendulum.
Cicogna G., Santoprete M.
Mel'nikov Method Revisited
2001, vol. 6, no. 4, pp. 377-387
We illustrate a completely analytic approach to Mel'nikov theory, which is based on a suitable extension of a classical method, and which is parallel and — at least in part — complementary to the standard procedure. This approach can be also applied to some "degenerate" situations, as to the case of nonhyperbolic unstable points, or of critical points located at the infinity (thus giving rise to unbounded orbits, e.g. the Keplerian parabolic orbits), and it is naturally "compatible" with the presence of general symmetry properties of the problem. These peculiarities may clearly make this approach of great interest in celestial mechanics, as shown by some classical examples.