Generalization of perturbation theory for a nonlinear system, losing a small parameter in the subregion where the solution changes
Abstract
The paper examines a nonlinear system of equations of motion for a material point (or charge) in a force field under the action of a continuous, initially small, perturbing force, whose relation to the gravitational (or attractive) force assumes such a form, that the system loses a small parameter in the course of time. The perturbation does not depend on fast time, but only on coordinates, velocities, and slow time. A method is proposed for obtaining an approximate solution unique for all regions where the small parameter is present and where it vanishes from the system.
 Publication:

Akademiia Nauk SSSR Doklady
 Pub Date:
 June 1976
 Bibcode:
 1976DoSSR.228..533L
 Keywords:

 Equations Of Motion;
 Gravitational Fields;
 Nonlinear Systems;
 Orbit Perturbation;
 Orbital Mechanics;
 Perturbation Theory;
 Astrodynamics;
 Center Of Gravity;
 Monotone Functions;
 Pendulums;
 Polar Coordinates;
 Astrodynamics