相关论文: Kozai Lidov Cycles = Simple Pendulum

The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D…

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…

A feasible experimental proposal to realize a non-dispersive quantum pendulum is presented. The proposed setup consists of an ultracold atomic cloud, featuring attractive interatomic interactions, loaded into a tilted ring potential. The…

This study explores the influence of a Stark-like perturbative potential on a quantum particle confined to a cylindrical surface (QPCS) and its implications for extra-dimensional theories. The QPCS framework is particularly relevant to…

Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the rotators are decoupled and we study the…

A small dipole oscillator moving along a circular trajectory in zero-point electromagnetic field ( ZPF ) and with a polarization normal to the rotation plane, is considered. Temporal periodicity conditions are imposed on ZPF, associated…

The Kibble-Zurek mechanism provides a description of the topological structure occurring in the symmetry breaking phase transitions, which may manifest as the cosmological strings in the early universe or vortex lines in the superfulid. A…

In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…

We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade…

We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole $\eps_2$, octupole $\eps_3$, and hexadecapole $\eps_4$) deformations of simple metal clusters with $90 \le N \le 550$ atoms in their…

The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…

We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpendicular to the orbital plane.…

The classical Kepler-Coulomb problem on the single-sheeted hyperboloid $H^{3}_1$ is solved in the framework of the Hamilton--Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or…

This work investigates different models of rotational dynamics of two rigid bodies with the shape of an ellipsoid, moving under their gravitational influence. The focus of this study is on their behavior, their linear stability, and…

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect…

The deformation of the classical action for a free relativistic particle recently suggested by A. Staruszkiewicz gives rise to a spin structure which constrains the values of the invariant mass and the invariant spin to be the same for any…

We study quantum mechanics problem described by the Schr\"{o}dinger equation with Kapitza pendulum potential, that is the asymmetric double-well potential on the circle. For the oscillatory states spatially localize around the two stable…

Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun")…

In this paper we revisit the construction by which the $SL(2,\mathbb{R})$ symmetry of the Euler equations allows to obtain the simple pendulum from the rigid body. We begin reviewing the original relation found by Holm and Marsden in which,…

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that…