Computational model for satellite periodic motion

Using the technique of inertial manifolds of ordinary differential equations in ℝn, we establish the existence of stable periodic motion of the satellite with a certain choice of controls. The presence of a two-dimensional inertial manifold allows us to reduce the problem of detecting such motions to the Poincare-Bendixson theory for dynamical systems on the plane. On the basis of the harmonic balance version, we obtain approximate analytical formulas for the corresponding closed trajectories and give accuracy estimates.Using the technique of inertial manifolds of ordinary differential equations in ℝn, we establish the existence of stable periodic motion of the satellite with a certain choice of controls. The presence of a two-dimensional inertial manifold allows us to reduce the problem of detecting such motions to the Poincare-Bendixson theory for dynamical systems on the plane. On the basis of the harmonic balance version, we obtain approximate analytical formulas for the corresponding closed trajectories and give accuracy estimates.