Adiabatic invariants, diffusion and acceleration in rigid body dynamics
From MaRDI portal
Publication:294485
DOI10.1134/S1560354716020064zbMath1377.70021MaRDI QIDQ294485
Ivan. S. Mamaev, Alexey V. Borisov
Publication date: 16 June 2016
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Free motion of a rigid body (70E15) Nonholonomic systems related to the dynamics of a system of particles (70F25) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)
Related Items (3)
Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics ⋮ Separatrix Crossing in Rotation of a Body with Changing Geometry of Masses ⋮ The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spherical robot of combined type: dynamics and control
- On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors
- How to control the Chaplygin ball using rotors. II
- The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
- The equations of the approximate theory of the motion of a rigid body with a vibrating suspension point
- Integrable cases in the dynamics of axial gyrostats and adiabatic invariants
- The dynamics of a rigid body colliding with a rigid surface
- Chaplygin ball over a fixed sphere: an explicit integration
- Generalized Chaplygin's transformation and explicit integration of a system with a spherical support
- How to control Chaplygin's sphere using rotors
- Comments on the paper by A. V. Borisov, A. A. Kilin, I. S. Mamaev ``How to control the Chaplygin ball using rotors. II
- The reversal and chaotic attractor in the nonholonomic model of Chaplygin's top
- Symmetries and reduction in nonholonomic mechanics
- Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
- Exact solution of a triaxial gyrostat with one rotor
- On the change in the adiabatic invariant on crossing a separatrix in systems with two degrees of freedom
- Regular and chaotic dynamics.
- Passage through a separatrix in a resonance problem with a slowly-varying parameter
- Static and time-dependent perturbations of the classical elliptical billiard.
- Chaplygin's ball rolling problem is Hamiltonian
- Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
- Rolling of a ball on a surface. New integrals and hierarchy of dynamics
- Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback
- Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals
- Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds
- Hamiltonicity and integrability of the Suslov problem
- Approximate equations of rotational motion of a rigid body carrying a movable point mass
- The problem of drift and recurrence for the rolling Chaplygin ball
- Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
- The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside
- The dynamics and control of a spherical robot with an internal omniwheel platform
- Properties of some chaotic billiards with time-dependent boundaries
- Geometrisation of Chaplygin's reducing multiplier theorem
- Fermi acceleration and adiabatic invariants for non-autonomous billiards
- Fast Fermi Acceleration and Entropy Growth
- Fermi acceleration in non-autonomous billiards
- On the motion of a heavy rigid body in an ideal fluid with circulation
- Motion of three vortices near collapse
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- A geometric criterion for adiabatic chaos
- Probability phenomena due to separatrix crossing
- Stable periodic motions in the problem on passage through a separatrix
- The presence and lack of Fermi acceleration in nonintegrable billiards
This page was built for publication: Adiabatic invariants, diffusion and acceleration in rigid body dynamics
