The Rigid-Body Dynamics of a Spinning Axisymmetric Body Subject to an Impulsive Mass Ejection
Technical Report,01 May 2018,31 Aug 2018
US Army Research Laboratory Aberdeen Proving Ground United States
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The rotational motion of bodies is a well-understood branch of dynamics. In this report, we apply those methods to study the problem of a spinning axisymmetric body that, in an instant, impulsively ejects a portion of its mass radially from the residual body. Not only is the residual body no longer axisymmetric, but the process of ejecting mass induces changes to the linear and rotational momentum of the residual body, as well as to its inertial properties. The ejection also produces precessive motion in the residual body. This report solves for the net state of the body in the immediate aftermath of the mass ejection. It then considers both an axisymmetric approximation to the residual motion, if the mass ejection is small, or, for the general case, solves the rotational momentum and energy equations in the body frame of reference, using a novel variation on a geometrical approach. The results of these analyses allow one to determine the range of precessive motion of the residual body.