Abstract
We consider the system of a rigid body in a weak gravitational field on the zero level set of the area integral and study its Poincare sets in integrable and nonintegrable cases. For the integrable cases of Kovalevskaya and Goryachev–Chaplygin we investigate the structure of the Poincare sets analytically and for nonintegrable cases we study these sets by means of symbolic calculations. Based on these results, we also prove the existence of periodic solutions in the perturbed nonintegrable system. The Chaplygin integrable case of Kirchhoff’s equations is also briefly considered, for which it is shown that its Poincare sets are similar to the ones of the Kovalevskaya case.
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