Corresponding author: Podchukayev Vladimir A., D. Sc., Professor, Chief Researcher, Institute of Problems of the Precise Mechanics and Control of RAS, Saratov, 410028, Russian Federation, Saratov State Law Academy, Saratov, 410056, Russian Federation, e-mail: sstu85@yandex.ru

Received on February 26, 2016
Accepted on March 14, 2016

On the basis of the new formulation of the problem of three bodies were obtained: 1) a new definition of the locus of the points of an equilateral hyperbola; 2) a new "dynamic formula of the golden section" to the representative point of a scalar field displacement of the center; 3) a new interpretation of the deleted point as the point preceding the transition to another branch of the rectangular hyperbola. It is shown that the author introduced the space of possible states of a dynamical system described by a scalar field as a hypersphere with a displaced center — quantized punctures offset center. That is in addition to the known quantization of time and the level of quantization is proposed a new method based on the quantization introduced by the author of the concept of the quantum motion, which is in contrast to the "photon" of theoretical physics is filled with rigorous mathematical content. Thus, the overall dimension of the state space and the space of possible states is (3n + 2). It is proved that the curvature of the space of possible states (phase space + hyperspace displacement of the center), as predicted by Einstein, is a geometric property of the scalar field. The space of possible states is a pulsating wave hyperspherical variable curvature center coordinates which are the algebraic sum of scalar waves of torsion on the branch of an equilateral hyperbola and scalar waves exponential motion. The proof is based on the quantum analogue of the Pythagorean theorem.

Keywords: scalar field, deleted point, center of displacement, quantum motion, direct motion, retrograde motion, hyper-space conditions, display space, hypersphere, pseudosphere

Acknowledgement: This work was supported by RFBR, project № 15-08-00181а.

For citation:
Podchukayev V. A. Quantum-Wave Dualism for Description of the Dynamic Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 7, pp. 453—457.
DOI: 10.17587/mau.17.453-457

To the contents