On the Angular Momentum of Rockets, Balloons, and Other Variable Mass Systems

TL;DR

This paper investigates the angular momentum behavior of variable mass systems like rockets and balloons, revealing that their angular momentum vector maintains a fixed direction in space, which could aid in orientation measurement.

Contribution

It demonstrates that the angular momentum vector of variable mass systems has a fixed spatial direction, offering a new reference frame for analyzing their orientation.

Findings

Angular momentum vector has a fixed direction in space.

Angular momentum magnitude is not conserved but direction is.

Provides a stationary reference frame for variable mass systems.

Abstract

Variable mass systems are a classic example of open systems in classical mechanics. The reaction forces due to mass variation propel ships, balloons, and rockets. Unlike free constant mass systems, the angular momentum of these systems is not of constant magnitude due to the change in mass. In this paper, we show that the angular momentum vector for such a system has a fixed direction in space and, thus, is partially conserved for both rigid and flexible, torque-free, variable mass systems. A potential use of this result is that it provides a suitable stationary reference frame against which the orientation of variable mass system could be measured.