Scientific paper ID 1417 : 2017/1

This article describes the concept of pseudo translational motion of rigid body (from Greek language ψευδο - lie). It is assumed that this motion represents a special case of his general movement, but with very little spin around the selected pole. Kinematics of pseudo translational movement has some specific features that are defined in this work. It facilitates the development of the corresponding dynamics, in particular, the small three dimensional vibrations of a rigid body.

It is known that in studying the spherical movement of a rigid body, especially in the courses of Theoretical Mechanics in the technical universities, Eulerian angles are used. (Leonhard Euler, 1707-1783). They describe and spherical components of the rotational movement of this rigid body. These angles have many advantages. They are particularly suitable for Celestial Mechanics. However, when considered a number of technical applications and tasks, particularly the movements of vehicles such as locomotives, wagons, automobiles, ships, airplanes and other, more appropriate to use Cardanian angles. (Girolamo Cardano, 1501-1576). They are very suitable for studying small three dimensional vibrations of the rigid body around its equilibrium position. That is the essence of this work. A specific linearization matrix of transition and angular velocity describing the spherical component of the overall motion of a rigid body is made. Finally, the ultimate goal of the study - the definition of the law of pseudo translational movement is reached. The study is leaded in a matrix form.