On the successive elimination of perturbation harmonics
Copyright policy )On the successive elimination of perturbation harmonics
The author presents a method of investigation of perturbations of an integrable Hamiltonian system of two degrees of freedom. He discusses its advantages and defaults in comparison with other applications. The main idea is based on the fact that a Hamiltonian with only one harmonic is integrable. This permits to eliminate it with help of results of Arnold (1963) and Henrard (1990). The advantages of the method are demonstrated in application to the Miranda-Umbriel problem in celestial mechanics.
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Fourier expansion, perturbations, resonances, action-angle variables, Celestial mechanics, chaotic motion, Hamiltonian systems, KAM theorem
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Fourier expansion, perturbations, resonances, action-angle variables, Celestial mechanics, chaotic motion, Hamiltonian systems, KAM theorem
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