Email this article SECOND DEGREE LOCAL INTEGRAL FOR ROTATING SYSTEMS. PART II
- Authors: Shamshiev F.T.1
-
Affiliations:
- National University of Uzbekistan named after Mirzo Ulugbek
- Issue: Vol 102, No 10 (2025)
- Pages: 950-960
- Section: Articles
- URL: https://journals.rcsi.science/0004-6299/article/view/355450
- DOI: https://doi.org/10.7868/S3034518925100074
- ID: 355450
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Abstract
The investigation of the existence of the quadratic local integral in stationary two-dimensional potential fields, initiated in the first part of the work, is ongoing. New mathematical relations are proposed, enhancing the understanding of the structure of functions describing the behavior of potential fields with arbitrary mass distributions. The rotation of the coordinate system is employed to simplify the equations and emphasize key features of the functional dependencies. Particular attention is given to arbitrary functions defining the potential and its derivatives under specific conditions. Their properties and possible solutions are analyzed. In addition, linear differential equations with polynomial and periodic solutions are studied. As a result of the work, theoretical results are formulated, which can be used for further analysis of quadratic integrals and for clarifying the differences between polynomials and other types of functions in broader mathematical models. The work is partially based on a talk presented at the Modern Stellar Astronomy 2024 conference.
About the authors
F. T. Shamshiev
National University of Uzbekistan named after Mirzo Ulugbek
Email: shamshiyev_f@nuu.uz
Tashkent, Uzbekistan
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