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vol 65 / August, 2022
Article

DOI 10.17586/0021-3454-2016-59-1-5-24

UDC 519.71

ANALYSIS OF SCALAR FIELDS OF DYNAMIC SYSTEMS

V. A. Podchukaev
Saratov State Academy of Law; Institute of Precision Mechanics and Control RAS; Professor


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Abstract. The principles of scalar field analysis for dynamic systems are presented as applied to point-body and rigid body. The space of the dynamic system solutions (the phase space) is shown to be a scalar field of the shape of a hypersphere with moveable or stable center as related to a fixed point on the hypersphere surface; the point is specified by the initial states vector. The scalar field movement is proved to have a reciprocating character, i.e. is a retrograde one relative to the movement in the state space supplemented, in the case of a shifted center, with the hyperbolic component of its drive. It is demonstrated that with a fixed center, the scalar field movement possesses the feature of normal Perron dichotomy. Conditions for exponential Perron dichotomy to take place, in the case of shifted center, are specified. The scalar field hidden parameters such as constant and variable mass and Lorentz force are taken into consideration; the analysis confirms the conservation laws for kinetic energy and pulse, as well as the magnetizing effect for moving rigid body.
Keywords: scalar field, hypersphere, shifted center, deleted point, hidden parameter, reciprocating motion of shifted center

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