Angular momentum of free variable mass systems is partially conserved

摘要

Variable mass systems are a classic example of open systems in classical mechanics with rockets being a standard practical example. Due to the changing mass, the angular momentum of these systems is not generally conserved. Here, we show that the angular momentum vector of a free variable mass system is fixed in inertial space and, thus, is a partially conserved quantity. It is well known that such conservation rules allow simpler approaches to solving the equations of motion. This is demonstrated by using a graphical technique to obtain an analytic solution for the second Euler angle that characterizes nutation in spinning bodies.