ABSTRACT: The small free three-dimensional vibrations of an asymmetrical rigid body connected with elastic elements and specialized dampers in this paper are studied. The influence of the arbitrary chosen coordinate system on the system of differential equations was determined. It has been shown that such a selected coordinate system can not be used to obtain the Eigen values and Eigen vectors. Analytical solutions depending on the degree of damping and the different Eigen values and Eigen vectors are developed. This article is intended for professionals and engineers working in the field of base isolation and protection against vibrations as well as for undergraduate and graduate students.
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