相关论文: Energy cost of dynamical stabilization: stored ver…

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in…

Comparative analysis of three stabilization mechanisms of unstable states of physical systems is presented in this review. These mechanisms are: the quantum Zeno effect, the stabilization of unstable states in an external fast oscillating…

We numerically investigate the stability and linear oscillatory behavior of a naturally diverging mass whose potential energy is harmonically modulated. It is known that in the Kapitza limit, i.e. when the period of modulation is much…

As realized by Kapitza long ago, a rigid pendulum can be stabilized upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilization is feasible in a variety of instances in…

The quantum states of the Kapitza pendulum are described within the effective potential obtained by the method of averaging over the fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using…

We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…

Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counterintuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with…

Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…

We present a pedagogical introduction to Floquet-Magnus theory through the classical example of Kapitza's pendulum - a simple system exhibiting nontrivial dynamical stabilization under rapid periodic driving. By deriving the equations of…

Dynamical perturbations modify the states of classical systems in surprising ways and give rise to important applications in science and technology. For example, Floquet engineering exploits the possibility of band formation in the…

When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…

How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite…

The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…

We study a friction controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in quantities such as displacement, traveled distance, and energy loss due to friction. Assuming…

We extend the theory of Kapitza stabilization within the complex domain, i.e. for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasi-energy spectrum is found to be entirely real-valued, however a…

We analyze the dynamics of a driven, damped pendulum as used in mechanical clocks. We derive equations for the amplitude and phase of the oscillation, on time scales longer than the pendulum period. The equations are first order ODEs and…

A generalization of the classical Kapitza pendulum is considered: an inverted planar mathematical pendulum with a vertically vibrating pivot point in a time-periodic horizontal force field. We study the existence of forced oscillations in…

An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the…

A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…

We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…