Appel’s function in the dynamics of rigid body systems

The effective formula for the Appel’s function calculation in the dynamics of a free rigid body is presented. The analysis of the relevant Appel’s system of dynamic equations is fulfilled. Appel’s dynamic equations are deduced for a flat chain of rigid bodies as well as for spatial chain. Some cases of possible simplification for systems of equations are considered. Systems of dynamic equations are supplemented by necessary kinematic equations.