Stability principle
https://doi.org/10.18384/2310-7251-2022-2-51-55
Abstract
Aim. The purpose of the paper is to prove that the principle of least action follows from the principle of stability.
Methodology. The paper proposes a formulation of the principle of stability of physical systems, which makes it possible to replace the principle of least action, since from the principle of stability follows the principle of least action.
Results. Two theorems are proved to achieve these goals.
Research implications. The work clarifies the origin of one of the basic physical laws, the principle of least action, and allows a different formulation of stability.
About the Author
T. F. Kamalov
Moscow Institute of Physics and Technology; Moscow Region State University
Russian Federation
Russian Federation
Timur F. Kamalov – Cand Sci (Phys.-Math.), Assoc. Prof., Department of Theoretical Physics; Assoc. Prof., Department of Theoretical Physics
Institutskii per. 9, Dolgoprudnyi 141700, Moscow region
ul. Very Voloshinoi 24, Mytishchi 141014, Moscow Region
References
1. Lyapunov A. M. The general problem of the stability of motion. In: International Journal of Control, 1992, vol. 55, iss. 3, pp. 531–534, DOI: 10.1080/00207179208934253.
2. Poincaré H. Sur les courbes définies par les équations différentielles (IV). In: Journal de Mathématiques Pures et Appliquées, 1886, vol. 2, pp. 151–218.
3. Kamalov T. F. Instability states and Ostrogradsky formalism. In: Journal of Physics: Conference Series, 2018, vol. 1051(1): XX International Meeting “Physical Interpretations of Relativity Theory 2017” (3–6 July 2017, Moscow, Russian Federation), pp. 012033. DOI: 10.1088/1742-6596/1051/1/012033.
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