Volokolamskoe sh. 4, Moscow, 125871 Russia
Moscow Aviation Institute
Bardin B. S., Chekina E. A.
On the Stability of Resonant Rotation of a Symmetric Satellite in an Elliptical Orbit
2016, vol. 21, no. 4, pp. 377-389
We deal with the stability problem of resonant rotation of a symmetric rigid body about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. In [1–3] the stability analysis of the above resonant rotation with respect to planar perturbations has been performed in detail. In this paper we study the stability of the resonant rotation in an extended formulation taking into account both planar and spatial perturbations. By analyzing linearized equations of perturbed motion, we found eccentricity intervals, where the resonant rotation is unstable. Outside of these intervals a nonlinear stability study has been performed and subintervals of formal stability and stability for most initial data have been found. In addition, the instability of the resonant rotation was established at several eccentricity values corresponding to the third and fourth order resonances. Our study has also shown that in linear approximation the spatial perturbations have no effect on the stability of the resonant rotation, whereas in a nonlinear system they can lead to its instability at some resonant values of the eccentricity.
Bardin B. S., Chekina E. A., Chekin A. M.
On the Stability of a Planar Resonant Rotation of a Satellite in an Elliptic Orbit
2015, vol. 20, no. 1, pp. 63-73
We study the Lyapunov stability problem of the resonant rotation of a rigid body satellite about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the satellite completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the above resonance rotation was started in [4, 6]. In the present paper, rigorous stability conclusions in the previously unstudied range of parameter values are obtained. In particular, new intervals of stability are found for eccentricity values close to 1. In addition, some special cases are studied where the stability analysis should take into account terms of degree not less than six in the expansion of the Hamiltonian of the perturbed motion. Using the technique described in [7, 8], explicit formulae are obtained, allowing one to verify the stability criterion of a time-periodic Hamiltonian system with one degree of freedom in the special cases mentioned.