ABSTRACT: In this paper, a pseudo translational motion of a free asymmetrical rigid body into an absolute reference system is studied. A private kind of Theorem of change of generalized body impulse is formulated. This theorem is called the Theorem of change of pseudo generalized body impulse. A private kind of Condensed Lagrange equation in matrix form is formulated. These equations are called Condensed Lagrange equations for the study of pseudo translational motion of the free asymmetrical rigid body. Using that theorem and those equations, the pseudo translational motion of the rigid body is successfully studied. The paper is theoretical, but it gives a base for a number of applications. For example, these are investigations of the motion, stability, and management of satellites. The other main application is free or forced small body vibrations. Moreover, the obtained formulas are appropriate for computer numerical integrations by contemporary mathematical programs.
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