Explicit forms of the rotational equations of motion for digital simulation

Abstract

The rotational acceleration for a rigid body has traditionally been represented by three simultaneous equations. Be cause of the computation time required for the iterative solution of simultaneous equations using a digital com puter, it is desirable to transform these equations to an explicit form for digital solution. The rotational equations are linear in the acceleration components. Thus, an explicit form can be obtained by either a determinate or a substi tution method. For problems where solution requires two or more of the cross-products-of-inertia terms, the determ inate method yields the most efficient equation form for digital solution. For the special case of body-plane sym metry (i.e., two cross-products-of-inertia terms are neg lected), the substitution method yields the most efficient form.