Related papers: Tippe Top Equations and Equations for the Related …
A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism $T$ is isomorphic to $T^{-1}$. We show that this problem is sufficiently general that asking it for…
Taylor-Couette flow between rotating cylinders is a classical problem in fluid mechanics and has been extensively studied in the case of two concentric circular cylinders. There have been relatively small number of studies in complex-shaped…
A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the…
In this paper, we study the dynamical instability of a collapsing object in the framework of generalized teleparallel gravity. We assume a cylindrical object with a specific matter distribution. This distribution contains energy density,…
When studying tropical cyclones using the $f$-plane, axisymmetric, gradient balanced model, there arises a second-order elliptic equation for the transverse circulation. Similarly, when studying zonally symmetric meridional circulations…
A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of the angular momentum expectation values…
We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…
Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of…
Real topological phases protected by the spacetime inversion (P T) symmetry are a current research focus. The basis is that the P T symmetry endows a real structure in momentum space, which leads to Z2 topological classifications in 1D and…
Strongly interacting spins underlie many intriguing phenomena and applications ranging from magnetism to quantum information processing. Interacting spins combined with motion display exotic spin transport phenomena, such as superfluidity…
We study the dynamics of the East model, comprising a chain of uncoupled spins in a downward-pointing field. Glassy effects arise at low temperatures $T$ from the kinetic constraint that spins can only flip if their left neighbour is up. We…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…
A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields…
Rotary dynamics of polarized composite particles as dipole rigid bodies is considered. It is described the Euler equations singularly perturbed by the radiation reaction torque. The Schott term is taken into account, and the reduction…
We consider the planar Taylor-Couette system for the steady motion of a viscous incompressible fluid in the region between two concentric disks, the inner one being at rest and the outer one rotating with constant angular speed. We study…
"Why does not a spinning top collapse?" is a puzzling question. Standard solution using angular momentum and torque is not intuitive enough. Thus intuitive explanations for the question have been proposed. We provide scaffolding for an…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J.…