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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The paper presents a study of a quasi-harmonic oscillator with dry and viscous friction. A simplified (Coulomb) mathematical model of dry friction is used. The method of approximate point mappings, which is an asymptotic method, is used to study the dynamics of the system. The problem of the existence of a periodic solution for the oscillator is considered as the problem of the existence of a fixed point for an analytically constructed point mapping that approximates with sufficient accuracy the point mapping generated by the trajectories of the system on the cutting surface. The stability of the desired periodic solution is also determined by the stability of the fixed point of the auxiliary point mapping. The question of the applicability of the results of the approximate study is raised.
Keywords:quasi-harmonic oscillator, dry friction, periodic mode, point mapping method, cutting surface, stability.
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Citation link:
Antonovskaya O. G., Besklubnaya A. V. TOWARDS THE STUDY OF THE DYNAMICS OF A QUASI-HARMONIC OSCILLATOR WITH COMBINED DRY AND VISCOUS FRICTION BY AN ASYMPTOTIC METHOD // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2025. -№06. -С. 48-52 DOI 10.37882/2223-2966.2025.06.04 |
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