Related papers: Plane Pendulum and Beyond by Phase Space Geometry

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 obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of the sine-Gordon and the sine hyperbolic-Gordon equations and…

Pendulums have long fascinated humans ever since Galileo theorized that they are isochronic with regards to their swing. While this simplification is useful in the case of small-angle pendulums due to the accuracy of the small-angle…

First-order perturbative calculation of the frequency-shifts caused by special relativity is performed for a charged particle confined in a Penning trap. The perturbed motion is approximated by the Jacobian elliptic functions which describe…

The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…

We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the…

In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…

We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…

The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…

There are considered some corollaries of certain hypotheses on the observation process of microphenomena. We show that an enlargement of the phase space and of its motion group and an account for the diffusion motions of microsystems in the…

For one dimensional maps the trajectory scaling functions is invariant under coordinate transformations and can be used to compute any ergodic average. It is the most stringent test between theory and experiment, but so far it has proven…

We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on…

We demonstrate that an effect other than anharmonicity can severely distort the spectroscopic signatures of quantum mechanical systems. This is done through an analytic calculation of the spectroscopic response of a simple system, a charged…

In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's…

There exist several theoretical motivations for primordial correlation functions (such as the power spectrum) to contain oscillations as a logarithmic function of comoving momentum k. While these features are commonly searched for in…

Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…

A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter…

We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…

Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…