On the Formulation of Equations of Rotational Motion for an N-Body Spacecraft

摘要

The equations of rotational motion of an arbitrary number of rigid bodies connected in either a cluster or tree configuration are developed using the momentum approach. In the momentum approach, the rotational equations for the rate of change of angular momenta of each of the bodies or composite bodies of the system of bodies are integrated to obtain a set of equations in angular momenta that are solved simultaneously to obtain the angular velocity for each body. The use of the momentum approach results in less complex equations that are easy to write and program and greatly simplifies the elimination of the troublesome interbody constraint torques. The momentum approach is first applied to develop, in detail, the equations for the cluster, a configuration in which each of an arbitrary number of bodies is connected to a central body. The digital solution of the cluster equations is discussed and a computational flow diagram is presented. The approach is then extended to the more general tree configuration in which an arbitrary number of composite bodies, each consisting of an arbitrary number of branch-connected bodies (no closed loops), is connected to a central body. The procedure for writing tree equations and obtaining their digital solution is described. The detailed equations for a five-body chain-cluster configuration, representing a dual-spin spacecraft having two moving fuel masses on the rotor and a two-degree-of-freedom damper on the platform, are presented. (Author)