Study of transition of spacecraft with asymmetry flat rotation to fluctuating motion while entering the atmosphere

Motion of Spacecraft with little asymmetry, restoring aerodynamic moment of which is described by Fourier series in the angle of attack with the first two sine and the first one-cosine terms, is considered in relation to its center of mass. Transition of Spacecraft flat rotation to fluctuation, conditioned by slow alteration of the coefficients of moment characteristics as well as by presence of little asymmetry and damping coefficients and their slow alteration, is studied. Analytical expression for the action integral, taken along the separatrixes that divide rotation and fluctuation regions of the system phase portrait, has been obtained. Analytical formulas for determination of the times of transition of rotation to fluctuation, and for critical angular velocity of the extra-atmosphere rotation, which causes prolonged body rotation (flat auto-rotation) when exceeded, have been derived.