Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals
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Publication:1941927
DOI10.1134/S1560354712060081zbMath1267.37066OpenAlexW2169774551MaRDI QIDQ1941927
Alexey V. Borisov, Alexei V. Bolsinov, Ivan. S. Mamaev
Publication date: 22 March 2013
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1134/s1560354712060081
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Constrained dynamics, Dirac's theory of constraints (70H45) Nonholonomic dynamical systems (37J60)
Related Items (22)
Regular and chaotic dynamics in the rubber model of a Chaplygin top ⋮ Spherical robot of combined type: dynamics and control ⋮ Qualitative analysis of the dynamics of a wheeled vehicle ⋮ Adiabatic invariants, diffusion and acceleration in rigid body dynamics ⋮ The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere ⋮ The Hess-Appelrot case and quantization of the rotation number ⋮ Rolling balls over spheres in $ \newcommand{\m}{\mathfrak m} {\mathbb{R}^n}$ ⋮ Topological analysis of an integrable system related to the rolling of a ball on a sphere ⋮ Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane ⋮ Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics ⋮ Comparative Analysis of the Dynamics of a Spherical Robot with a Balanced Internal Platform Taking into Account Different Models of Contact Friction ⋮ The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint ⋮ Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$ ⋮ Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors ⋮ Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane ⋮ Invariant Submanifolds of Genus 5 and a Cantor Staircase in the Nonholonomic Model of a Snakeboard ⋮ The Jacobi integral in nonholonomic mechanics ⋮ The Hess-Appelrot system and its nonholonomic analogs ⋮ Nonintegrability and obstructions to the Hamiltonianization of a nonholonomic Chaplygin top ⋮ The dynamics and control of a spherical robot with an internal omniwheel platform ⋮ Dynamics and control of an omniwheel vehicle ⋮ Demchenko’s nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis
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