Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere
From MaRDI portal
Publication:4632032
DOI10.1088/1361-6544/aafcddzbMath1410.37060arXiv1805.10610OpenAlexW3099502355WikidataQ128058565 ScholiaQ128058565MaRDI QIDQ4632032
Borislav Gajić, Božidar Žarko Jovanović
Publication date: 25 April 2019
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.10610
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesics in global differential geometry (53C22) Nonholonomic systems related to the dynamics of a system of particles (70F25) Linear and affine connections (53B05) Nonholonomic dynamical systems (37J60)
Related Items
Generalisation of Chaplygin’s reducing multiplier theorem with an application to multi-dimensional nonholonomic dynamics, Gyroscopic Chaplygin systems and integrable magnetic flows on spheres, Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$, Integrability and dynamics of the \(n\)-dimensional symmetric Veselova top, The geometry of nonholonomic Chaplygin systems revisited, Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere, Demchenko’s nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dynamics of the Chaplygin sleigh on a cylinder
- Invariant nonholonomic Riemannian structures on three-dimensional Lie groups
- The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
- The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards
- Integrable Euler top and nonholonomic Chaplygin ball
- Projective dynamics and first integrals
- A completely integrable mechanical system
- Chaplygin ball over a fixed sphere: an explicit integration
- Rubber rolling over a sphere
- Rolling of a non-homogeneous ball over a sphere without slipping and twisting
- Geometric control and numerical aspects of nonholonomic systems
- Non-holonomic Chaplygin systems
- Invariant measures of modified LR and L+R systems
- Integrable nonholonomic systems on Lie groups
- Reduction of some classical non-holonomic systems with symmetry
- Affine connections and distributions with applications to nonholonomic mechanics
- The Wagner curvature tensor in nonholonomic mechanics
- Integrable discretization and deformation of the nonholonomic Chaplygin ball
- Understanding reversals of a rattleback
- Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems
- Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces
- Integrability and dynamics of the \(n\)-dimensional symmetric Veselova top
- Unimodularity and preservation of volumes in nonholonomic mechanics
- Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts
- Regular and chaotic dynamics in the rubber model of a Chaplygin top
- Geodesics on the ellipsoid and monodromy
- Geometrisation of Chaplygin's reducing multiplier theorem
- Newton's Law and Integrability of Nonholonomic Systems
- On the geometry of generalized Chaplygin systems
- Invariant measures of nonholonomic flows with internal degrees of freedom
- Rolling balls over spheres in $ \newcommand{\m}{\mathfrak m} {\mathbb{R}^n}$
- Moving energies as first integrals of nonholonomic systems with affine constraints
- Noether symmetries and integrability in time-dependent Hamiltonian mechanics
- On geometrization of motion of some nonholonomic systems
- The Weitzenböck connection and time reparameterization in nonholonomic mechanics
- LR and L+R systems
- Rolling of a Rigid Body Without Slipping and Spinning: Kinematics and Dynamics
- On the Transformation of the Equations of Dynamics
