Three dimensional linear motion transformation in a higher order dimensional space |
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Authors: | YTs Tsankov AlB Kazakoff |
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Institution: | 1. Faculty of Mathematics and Informatics, The University of Sofia, “St. Kliment Ohridski”, Bulgaria;2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria |
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Abstract: | The objective of the work presented in this paper is an attempt at solving and transforming of the known from the classical mechanics three dimensional – single mass mathematical and mechanical vibration models in a higher order dimensional space with any virtual sectional curvature – positive or negative, constant or variable. The object of the investigation is a class of three dimensional surfaces. The aims of the work presented in this paper are to illustrate the performance of the common algorithm in three dimensional linear motion transformation, that means to transform 3D space in a higher order dimensional space and a comparison is derived on the behavior of the common algorithm depending on the surface properties. A characterization of the Riemannian Manifolds is performed by means of curvature operators in the three dimensional solution. The computer codes Mathematica and MATLAB are used in the numerical simulation. The system motion is investigated in a 3-D qualitative aspect in time and frequency domain. The application can be in topology when geodesists make snap shots of the surface profile, then the curved lines can be analyzed and transformed in the desired space dimension. Any kind of a trajectory of motion can be transformed successfully in a higher order dimensional space and vice verse by means of applying of the common algorithm. |
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Keywords: | Classical mechanics vibration solutions 3-D Mechanical and mathematical modeling Riemannian Manifolds Higher order dimensional space Positive and negative sectional curvature Computer simulation |
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