The use of Rodrigues–Hamilton parameters in interpreting the motion of a rigid body with a fixed point

The connection between the different methods of interpreting the motion of a body with a fixed point is investigated. A new form of the equations of a stationary angular velocity hodograph is obtained that allows the Poinsot method to be applied using Rodrigues–Hamilton parameters. The properties of the kinematic parameters are studied for the precessing and isoconic motions of the body. The precessing motions in Dokshevich's solution and the isoconic motions in Steklov's solution are considered.