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

Some spacecraft can be modeled as torque-free spinning gyrostats, and in practice these are often designed as nominally symmetric about a principal axis with an angular momentum aligned with the same axis; as actually constructed, they are almost-symmetric, almost-aligned. A general solution for the polhodes, known as a computational algorithm though not as a literal expression, does not simplify in the slightly off-nominal case. The present paper develops an accurate literal expression for polhodes sufficiently close to an osculation point in the latter case; errors in the endcap solutions are of the order of 1% for the endcap in several test problems examined.