On the extremality hypothesis of stable resonance motions (Q1064094)

On the basis of a proposed approximate method of determining the mean values of functions of the coordinates and time on almost-integrable trajectories of dynamic systems, the force function and kinetic energy are averaged in the following problems: the motion of a material point in the neighbourhood of triangular points of libration of the plane circular restricted three-body problem, the motion of a physical pendulum with a rapidly oscillating point of suspension in the neighbourhoods of the lower and upper equilibrium positions. Preference is shown for the following hypotheses: the minimum of the averaged potential (V. V. Beletskij hypothesis), kinetic, and total energy of the mechanical system at stable, isolated, synchronous motions.