A New Solution for the Classical Problem of a Rigid Body Motion ‎in a Liquid

We consider the problem of the motion of a rigid body-gyrostat immersed in an incompressible ideal fluid. Based on Yehia’s study [1, 2], the equations of the motion of the problem are introduced and they are reduced to the orbital equation. This reduced equation may be used to study the stability of certain motions of the body [3] and to obtain solutions for the classical problems in rigid body dynamics [4]. Using the orbital equation, a single new solution of the considered problem is obtained in which the angle between the body axis of symmetry and the vertical axis is constant.