Work

Structural stability of logarithmic spirals in control problems with second-order singular extremal

Year: 2025

Type: article

Abstract: A nonlinear perturbation of generalization of the Fuller problem with controls in a disk is considered. The structural stability of logarithmic spirals is studied. It was shown that if perturbations are small with respect to the action of the symmetry group of the unperturbed problem, then in the neighborhood of a singular second-order solution, extremals in the form of logarithmic spirals are preserved. The constructed extremals arrive at a singular extremal in a finite time, while the controls make an infinite number of revolutions along the circle.

Source: Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki

DOI: 10.35634/vm250107

Authors: M.I. Ronzhina, L.A. Manita

Institutions: Gubkin Russian State University of Oil and Gas, Moscow State Institute of Electronics and Mathematics, National Research University Higher School of Economics

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408838899

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