相关论文: Study of normal modes and symmetry breaking in a t…

The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but…

A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…

We describe a simple mechanical system that involves Spontaneous Symmetry Breaking. The system consists of two beads constrained to slide along a hoop and attached each other through a spring. When the hoop rotates about a fixed axis, the…

The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…

This paper considers a nonlinear spherical pendulum whose suspension point performs high-frequency spatial vibrations. The dynamics of this pendulum can be described by averaging its Hamiltonian over phases of vibrations. Rotationally…

Spontaneous symmetry breaking is central to our understanding of physics and explains many natural phenomena, from cosmic scales to subatomic particles. Its use for applications requires devices with a high level of symmetry, but engineered…

The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…

This paper shows the study of interesting mechanical properties of Wilberforce pendulum. Analyzing qualitatively of the pendulum, it is able to know how the phenomenon occurs. By setting of the quantitative model, equation of the motion is…

We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…

This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase rotations are realized. Asymptotic theory is developed that…

We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…

We present the results of linear stability of a damped coplanar double pendulum and its non-linear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude $a$ and frequency $\omega $. A double…

A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the…

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…

Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined…

Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar…

The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…

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…

We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev…