Four Hamiltonian Systems

Table of contents :
1.1.1 Description……Page 1
1.1.2 The 2-Mode……Page 3
1.1.3 The 3-Mode……Page 8
1.2.1 Perturbed Kepler Systems……Page 9
1.2.2 Description……Page 10
1.2.3 Normalization and Reduction……Page 11
1.2.4 Energy Momentum Map……Page 12
1.3.1 A Spherical Pendulum Model for Floppy Triatomic Molecules……Page 14
The Linear Spherical Pendulum……Page 15
Quadratic Spherical Pendulum with $V (z) = -z^2$……Page 16
General Situation……Page 17
1.4 The 1: – 2 Resonance System……Page 18
Reduction of the m:n Resonance……Page 19
Reduction of the m: – n Resonance……Page 20
1.4.3 Fractional Monodromy in the 1: – 2 Resonance System……Page 22