Periodic solutions of the problem of a rigid body moving about the centroid in central Newtonian field

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Center Of Mass, Equations Of Motion, Liapunov Functions, Newton Methods, Rigid Structures, Equilibrium Methods, Gyroscopic Stability, Moments Of Inertia, Motion Stability

Scientific paper

The equations of motion of rigid body about a fixed point in central Newtonian field are reduced to the equations of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid. The construction of periodic solutions near equilibrium points are carried out using Liapunov's theorem of holomorphic integral, and the necessary and sufficient conditions for the stability of the system are obtained.

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