Abstract:
This paper presents a method for integrating the equations of motion of a rigid body having
a fixed point in three homogeneous force fields. It is assumed that under certain conditions these
equations admit an invariant relation that is characterized by the following property: the velocity
of proper rotation of the body is twice as large as the velocity of precession. The integration of
the initial system is reduced to the study of three algebraic equations for the main variables of
the problem and one differential first-order equation with separating variables.
Keywords:three homogeneous force fields, precessional motions, invariant relation
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