Dynamics of body separation—analytical procedure

Abstract

In this paper, an analytical procedure for the determination of the dynamic parameters of a remainder body after mass separation is developed. The method is based on the general principles of momentum and angular momentum of a body and system of bodies. The kinetic energy of motion of the whole body and also of the separated and remainder body is considered. The derivatives of kinetic energies with respect to the generalized velocity determine the velocity and angular velocity of the remainder body. To confirm the proposed procedure, the results are compared with those obtained using the method of momenta and angular momenta. In the paper, the theorem about increase of kinetic energies of the separated and remainder bodies for perfectly plastic separation is proved. The increase of the kinetic energies correspond to the relative velocities and angular velocities of the separated and remainder bodies. As an example, the mass separation from a pendulum is considered. The kinematic properties of the remainder pendulum are obtained using the analytic procedure. The results are in agreement with those obtained by applying the basic principles of Newton's mechanics.

Geometry of motion and nutation stability of free axisymmetric variable mass systems

“…The second generation of studies was more expansive. Apart from revisiting the derivation of the equations of motion of continuous mass varying systems [5][6][7], attention has also been paid to algorithm development for simulating rigid [8] and flexible systems with mass variation [9,10], as well as analyses of systems with discontinuous mass variation [11,12].…”