ABSTRACT: The article introduces the concept of pseudo translational motion for a free ideal rigid body (from the Greek ψευδο – lie). This motion is assumed to represent a particular case of its general motion, but with very little rotation about a chosen pole. The kinematics of pseudo-translational motion has some specific features that are defined herein work. It facilitates the development of relevant dynamics, and more specifically, of the small spatial oscillations of the rigid body. It is known that when studying the spherical motion of an ideal solid body, traditionally, Euler angles are used. (Leonhard Euler, 1707-1783). They also describe the spherical component of the general motion of a given rigid body. These angles have many advantages. They are particularly suitable for Celestial Mechanics. When, however, a number of technical applications and tasks are considered, such as movements of means of transport, for example, locomotives, wagons, cars, ships, planes, and others, it is better to use gimbal angles. (Girolamo Cardano, 1501-1576). They are also very suitable when studying the small spatial oscillations of a rigid body around its equilibrium position. This is the essence of the present work. A specific linearization was performed on the transition and angular velocity matrices that describe the spherical component of the total motion of a given rigid body. Finally, the ultimate goal of the research is reached – defining the law of pseudo-translational motion. The study is conducted in matrix form.
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