Related papers: Monodromy in the resonant swing spring
In this letter we present a general classification of integrable models of identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our constructive proof of integrability provides a solution scheme for the equations…
A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown…
We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde…
The work concerns the spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system. The existence of chaotic oscillations was demonstrated in a wide range of changes in the parameters of the model. The model of such a…
The classical spin system consisting of three spins with Heisenberg interaction is an example of a completely integrable mechanical system. In this paper we explicitly calculate thermodynamic quantities as density of states, specific heat,…
We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase…
The relativistic precession model (RPM) is widely-considered as a benchmark framework to interpret quasi-periodic oscillations (QPOs), albeit several observational inconsistencies suggest that the model remains incomplete. The RPM ensures…
Mean-motion resonances (MMRs) are likely to play an important role both during and after the lifetime of a protostellar gas disk. We study the dynamical evolution and stability of planetary systems containing two giant planets on circular…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
The intakes of air-breathing high-speed flying vehicles produce a large share of the thrust propulsion. Furthermore, the propulsion performance of these engines increases when the single-ramp intake is replaced with a multiple-ramps intake.…
We study the fully itinerant dynamics of ultracold but nondegenerate polar molecules with a spin-$1/2$ degree of freedom encoded into two of their electric field dressed rotational states. Center of mass molecular motion is constrained to…
We obtain normal forms for symmetric and for reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized \Henon normal form of Friedland and Milnor. We…
The widespread phenomena of multistability is a problem involving rich dynamics to be explored. In this paper, we study the multistability of a generalized nonlinear forcing oscillator excited by $f(x)cos \omega t$. We take Doubochinski's…
Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, flight systems consisting elastic elements coupled to nonlinear, unsteady…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…
We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in a constriction of nanometric dimensions, the coupling…