On the extremality hypothesis of stable resonance motions
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 neighbourhoo...
Saved in:
| Published in | Journal of applied mathematics and mechanics Vol. 48; no. 4; pp. 489 - 492 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
1984
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | 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. Beletskii hypothesis), kinetic, and total energy of the mechanical system at stable, isolated, synchronous motions. |
|---|---|
| ISSN: | 0021-8928 0021-8928 |
| DOI: | 10.1016/0021-8928(84)90021-2 |