New Methods of Celestial Mechanics

Author(s): Jan Vrbik

DOI: 10.2174/978160805187811001010079

Resonances

Pp: 79-102 (24)

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Abstract

SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.

Abstract

Resonances occur when period of the perturbing force is commensurable with the perturbed body’s orbital motion (2/1 resonance corresponds to a perturbing force whose one cycle is completed in two orbits of the perturbed body; two cycles are completed during one orbit in the case of 1/2 resonance, etc.). They constitute a rather special (and difficult) category of time-dependent perturbations, as we demonstrate using several examples of an asteroid perturbed by Jupiter’s gravitational pull. We start with the 1/1 resonance, which has some unique features, not shared by other resonances.

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