Antonovskaya Olga Georgievna (Candidate of Physical and Mathematical Sciences, Associate Professor,
Federal State Budgetary Educational Institution of Higher Education “Nizhny Novgorod State University of Architecture and Civil Engineering”
)
Besklubnaya Antonina Vyacheslavovna (Candidate of Pedagogical Sciences,
Federal State Budgetary Educational Institution of Higher Education “Nizhny Novgorod State University of Architecture and Civil Engineering”
)
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Oscillators are widely used in nature and technology. When considering nonlinear oscillators, it becomes necessary to use asymptotic methods, since, as a rule, there are no exact methods for solving the corresponding differential equations. This article presents the main points of application of the method of approximate point mappings to the study of the dynamics of a quasi-harmonic oscillator of the Van der Pol type. The approximate point mapping is based on the method of successive approximations. Since the sequence functions of the constructed point mapping are explicit, the problem admits of an analytical solution. And the question of the existence of a periodic solution for a quasi-harmonic oscillator is solved as a question of the existence for an approximately constructed point mapping fixed points with one or another type of stability.
Keywords:quasi-harmonic oscillator, point mapping method, phase space, secant plane, asymptotic research methods.
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Citation link:
Antonovskaya O. G., Besklubnaya A. V. TO STUDY A QUASI-HARMONIC OSCILLATOR OF THE VAN DER POL TYPE BY THE METHOD OF APPROXIMATE POINT MAPPINGS // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2025. -№07. -С. 41-45 DOI 10.37882/2223-2966.2025.07.02 |
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