Nonintegrability and obstructions to the Hamiltonianization of a nonholonomic Chaplygin top

DOI10.1134/S1064562414060192zbMath1316.37033MaRDI QIDQ2254126

Ivan. A. Bizyaev

Publication date: 4 February 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (10)

Regular and chaotic dynamics in the rubber model of a Chaplygin top ⋮ Spherical robot of combined type: dynamics and control ⋮ The Hess-Appelrot case and quantization of the rotation number ⋮ Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics ⋮ The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint ⋮ Invariant Submanifolds of Genus 5 and a Cantor Staircase in the Nonholonomic Model of a Snakeboard ⋮ Dynamics of a spherical robot with variable moments of inertia and a displaced center of mass ⋮ The Jacobi integral in nonholonomic mechanics ⋮ The Hess-Appelrot system and its nonholonomic analogs ⋮ Dynamics and control of an omniwheel vehicle

Cites Work

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• On the nonlinear Poisson bracket arising in nonholonomic mechanics
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• Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane
• Precession and recession of the rock'n'roller
• On the Routh sphere problem
• Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's top

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