Nonlinear free oscillations of a rotating solid body in a Newtonian force field

Nonlinear free oscillations of a rotating axisymmetrical solid body are considered with respect to the center of mass and with the body moving in a Newtonian force field. To construct periodic solutions of nonlinear differential equations of the motion, some algorithms, which are based on a modification of the extension method of solution with respect to a parameter, are used. The stability of nonlinear oscillations of the rotating solid body are studied with respect to stationary motions, some amplitude-frequency characteristics and forms of oscillations of the body are formulated for different values of its inertial parameters.