Heavy rigid body

Abstract

According to a theorem of Euler [1] the general displacement of a rigid body with one fixed point is a rotation about some axis through this point. The position of a rigid body is completely determined by locating a rectangular coordinate trihedral fixed in the rigid body relative to a rectangular coordinate trihedral fixed in space. If the fixed point is taken as a common origin of the body and space trihedrals, then the orientation of the body in space can be described in terms of the direction cosines of the body axes relative to the space axes. Among the nine direction cosines only three are independent. Therefore we must use some set of three independent functions of the direction cosines to specify the position of the rigid body. A number of such sets of independent variables have been described in the literature, the most important and useful being the Euler [2] angles.