ABSTRACT: In this paper, a general motion of the free asymmetrical rigid body to an absolute coordinate system is studied. The rotating component of body motion is described by using Cardan angles. A new kind of theorem is formulated. It is called the Theorem of change of generalized body impulse. New kinds of differential Lagrange equations of the second gender are formulated. These are called Condensed Lagrange equations. Using that theorem and those equations, the general motion of the rigid body is successfully studied. The paper is theoretical, but it gives a base for a number of applications, for example, applications in the field of body overflow in the fluid area and in the field of body vibrations. Moreover, the obtained formulas are appropriate for computer numerical integrations by contemporary mathematical programs.
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