Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest are the reaction wheels in satellites, wheels on a car, propellers on a helicopter and flywheels in machines. Each such body spins about one of its principal axes and around its center of mass. Current recursive solution methods treat all bodies in the system identically. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order O(N-m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.