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An analytical approach to attitude determination of a spinning satellite

The attitude of a spinning satellite, specified in terms of the three Eulerian angles, is related to the angular velocity components in body-fixed co-ordinates by three coupled first-order non-linear differential equations. In general, these equations, being complex, are not amenable to analytical techniques. This study presents a new analytical approach to the analysis of these equations by first reducing the problem to the study of a single second-order non-linear differential equation and then establishing its equivalence with a second-order linear differential equation for the case of the satellite spinning with constant angular velocity components. The solution of this equivalent linear equation is then used to obtain the Eulerian angles.