相关论文: Linearisation of Simple Pendulum

We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604].…

The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…

Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…

This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…

The relative classical motion of membranes is governed by an equation of the form D(hessian D separation)=riemann times separation times momentum. This is a generalization of the geodesic deviation equation and can be derived from a simple…

The classical walking behaviors of a single atom in an amplitude-modulated standing wave lattice beyond the internal dynamics are investigated. Based on a simple effective model, we identify a diversity of dynamic regimes of atomic motion…

This study is on small oscillations of a heavy symmetric top. A different method than previous works is applied, and differently from previous works, the explicit formulas for the amplitudes for oscillations are given. This method can be…

In this work we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal…

We present a scheme of self-propelling liquid droplets which closely mimics the locomotion of some protozoal organisms, so-called squirmers. In contrast to other schemes proposed earlier, locomotion paths are not self-avoiding, since the…

We discuss several steady-state rotation and oscillation modes of the planar parametric rotator and pendulum with damping. We consider a general elliptic trajectory of the suspension point for both rotator and pendulum, for the latter at an…

A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is…

From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…

The kinematics of the Solar zenith passage on the Earth was shown as a simple harmonic motion. This analytical model used the uniform circular motion to describe the Earth's rotation relative to its axis and relative to the Sun, also this…

We show that the natural motion of particles in continuous space-time (CSTM) is not classical continuous motion (CCM), but one kind of essentially discontinuous motion, the wave function in quantum mechanics is the very mathematical complex…

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 examine the problem of motion of an oscillating mass object provided no external force is applied to it. Calculations directly lead to the conclusion that the body accelerates in each system of reference except for the rest reference…

We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…

A compound pendulum of simple geometry was built from a lightweight rod to which a pair of masses are clamped, one above and the other below the axis of rotation. By making the position of the upper mass variable, it was found that the…

We consider a chain of coupled pendula pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. The common strings in each pair are modulated periodically by an external force. In the…

We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in…