Related papers: Finding the period of a simple pendulum

This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric…

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…

This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…

This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and…

While adhering to the formalism of Special and General Relativity, this paper considers the interpretation of clock rates and the rating of clocks in detail. We also pay particular attention to the crucial requirement of reciprocity between…

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…

A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…

Tunneling is one of the most bizarre phenomena in quantum mechanics. An attempt to understand it led to the next natural question of how long does a particle need to tunnel a barrier. The latter gave rise to several definitions such as the…

Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…

Spacetime emergence from entanglement proposes an alternative to quantizing gravity and typically derives a notion of distance based on the amount of mutual information shared across sub-systems. Albeit promising, this program still faces…

A finite sequence of equidistant samples (a sample train) of a periodic signal can be identified with a point in a multi-dimensional space. Such a point depends on the sampled signal, the sampling period, and the starting time of the…

Simple Hamiltonian systems, such as mathematical pendulum or Euler equations for rigid body, are solved without computation. It is nothing but a joke but maybe you will find it nice.

The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows…

Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…

We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The…

We investigate the dependence of the displacements of a molecular motor embedded inside a glassy material on its folding characteristic time. We observe two different time regimes. For slow foldings (regime I) the diffusion evolves very…

For simple electromagnetic models of a rod and a clock, a change of the shape of the rod and of the rate of the clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle…

We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…

We discuss the fundamemtal constants in the Standard Model of particle physics, in particular possible changes of these constants on the cosmological time scale. The Grand Unification of the observed strong, electromagnetic and weak…

In the paper, elements of the system theory of time are presented, mathematical models for time are constructed, and various properties are deduced from the main principles of the system theory of time. This theory is a far-reaching…