Angular Momentum of a Torque-Free Deforming Axisymmetric Gyro

Abstract

Attitude drift and attitude stability studies of torque-free gyros involve an angular momentum that is constant in magnitude and direction. The problem is to find suitable coordinates to describe the gyro’s behavior, and then to express the (constant) angular momentum in these coordinates. Expressions for small deformation are available. In the present paper the expression, in floating coordinates, for the angular momentum of a torque-free deforming axisymmetric gyro in terms of inertia moments and angular velocity components is extended to beyond small deformations. The angular momentum expression is written first in its general form. Thqn the angular momentum is expressed in matrix form for the calculation of angular momentum components for arbitrarily large deformation. Finally, three models are presented to illustrate the application of the angular momentum expression obtained.