Spin of an almost-axial, almost-symmetric, torque-free gyrostat near an osculation condition

Abstract

Some spacecraft can be modeled as torque-free spinning gyrostats, and in practice these often are designed as nominally symmetric about a principal axis with an internal angular momentum aligned with the same axis. As actually constructed, they are almost-symmetric, almost-aligned. A general solution for the polhodes is known as a computational algorithm, though not as a literal expression. The general solution does not simplify in the slightly off-nominal case. This paper develops an accurate literal expression for polhodes sufficiently close to an osculation points in the latter case. Errors in the endcap solutions are of the order of I % for the end-cap in the several test problems examined.