On Linear Invariant Manifolds in the Generalized Problem of Motion of a Top in a Magnetic Field
Differential equations describing the rotation of a rigid body with a fixed point under the influence of forces generated by the Barnett–London effect are analyzed. They are a multiparametric system of equations. A technique for finding their linear invariant manifolds is proposed. With this technique, we find the linear invariant manifolds of codimension 1 and use them in the qualitative analysis of the equations. Computer algebra tools are applied to obtain the invariant manifolds and to analyze the equations. These tools proved to be essential.
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