Analysis of a Simple Mechanism to Deplete the Kirkwood Gaps

Abstract

In most applications resonance problems are implicitely or explicitely modelized by the Fundamental Model of Resonance i.e. the pendulum, characterized by its Hamiltonian function:

$$H = \frac{a}{2}{I^2} - b cos \psi $$

(1)

This reduction is performed in two steps: first, the action-angles variables are introduced to get a “one degree of freedom” Hamiltonian system, given by (2):

$$K = {k_o}(S) + \varepsilon {K_1}(S,s)$$

(2)

where K₁ is 2π — periodic in s (the resonant angle).