In this paper, the dynamics of the two-gyro Anschütz compass in two cases, i.e. the earth spin velocity and zero vehicle velocity case, as well as the earth spin velocity and non-zero vehicle case, are studied. The detailed exact equations of motion of this compass are obtained by Lagrange's equations. The system is studied by the linear approximation method, and these equations are solved as eigenvalue problems. The stabilities of these motions are also discussed. The analytical stabilities for two cases from the linear approximation method are checked by the numerical solutions.
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