Stability of autonomous systems in the presence of several resonances
Abstract
A stability analysis is carried out for the equilibrium position of an autonomous system of ordinary differential equations in the critical case of n pairs of pure imaginary roots plus several resonance relations. For a special class of systems, stability and instability conditions for the equilibrium positions in the first nonlinear order are obtained. For illustration, the results are applied to the problem of satellite fluctuations about the equilibrium position along a circular orbit.
- Publication:
-
Prikladnaia Matematika i Mekhanika
- Pub Date:
- April 1979
- Bibcode:
- 1979PriMM..43..229Z
- Keywords:
-
- Celestial Mechanics;
- Motion Stability;
- Orbit Perturbation;
- Resonance;
- Satellite Orbits;
- Circular Orbits;
- Differential Equations;
- Hamiltonian Functions;
- Systems Stability;
- Theorem Proving;
- Astrodynamics