Two non-holonomic integrable problems tracing back to Chaplygin

DOI10.1134/S1560354712020074zbMath1252.76056OpenAlexW2000228981MaRDI QIDQ691229

Alexey V. Borisov, Ivan. S. Mamaev

Publication date: 30 November 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354712020074

zbMATH Keywords

integrabilityinvariant measurequadraturegyroscopenon-holonomic constraintcoupled rigid bodies

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Vortex methods applied to problems in fluid mechanics (76M23)

Related Items (13)

A top on a vibrating base: new integrable problem of nonholonomic mechanics ⋮ Spherical robot of combined type: dynamics and control ⋮ On the motion of a mechanical system inside a rolling ball ⋮ The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere ⋮ Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target ⋮ The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint ⋮ Stabilization of steady rotations of a spherical robot on a vibrating base using feedback ⋮ Controlled motion of a spherical robot with feedback. II. ⋮ Stability and stabilization of steady rotations of a spherical robot on a vibrating base ⋮ Intermediate Toda systems ⋮ Controlled motion of a spherical robot with feedback. I ⋮ The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside ⋮ Different models of rolling for a robot ball on a plane as a generalization of the Chaplygin ball problem

Cites Work

• Unnamed Item
• Chaplygin ball over a fixed sphere: an explicit integration
• Generalized Chaplygin's transformation and explicit integration of a system with a spherical support
• On some generalization of the area theorem with applications to the problem of rolling balls. Translated from the Russian 1897 original
• The dynamics of Chaplygin ball: the qualitative and computer analysis
• Nonholonomic manipulators.
• Rolling of a homogeneous ball over a dynamically asymmetric sphere

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