Related papers: Oscillations bounded by the simple pendulum and th…
We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation…
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
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…
Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
We use Lagrangian formalism and jet spaces to derive a computational model to simulate multibody dynamics with holonomic constraints. Our approach avoids the traditional problems of drift-off and spurious oscillations. Hence even long…
Friction is a complex phenomenon that is of paramount importance in everyday life. We present an easy-to-build and inexpensive experiment illustrating Coulomb's law of kinetic friction. The so-called friction, or Timoshenko, oscillator…
In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
Creating a simulation of a system enables the tuning of control systems without the need for a physical system. In this paper, we employ Lagrangian Mechanics to derive a set of equations to simulate an inverted pendulum on a cart. The…
Precision sensing and manipulation of milligram-scale mechanical oscillators has attracted growing interest in the fields of table-top explorations of gravity and tests of quantum mechanics at macroscopic scales. Torsional oscillators…
In this paper, we study the generation and propagation of oscillatory solutions observed in the widely used Lorenz 96 (L96) systems. First, period-two oscillations between adjacent grid points are found in the leading-order expansions of…
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…
The Foucault Pendulum is a Spherical Pendulum of fixed length with two angular degrees of freedom, attached to a suspension which rotates once a day around the Earth axis at a distance essentially set by Earth radius and the geodetic…
The motion of a driven planar pendulum with vertically periodically oscillating point of suspension and under the action of an additional constant torque is investigated. We study the influence of the torque strength on the transition to…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The evaluation of variation in oscillation time period of a simple pendulum as its mass varies proves a rich source of discussion in a physics class-room, overcoming erroneous notions carried forward by students as to what constitutes a…
We present a formalism for investigating the interaction between pmode oscillations and convection by analyzing realistic, three-dimensional simulations of the near-surface layers of the solar convection zone. By choosing suitable…
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,…
The nearly-incessant free oscillations of the Earth (not the larger, long-lived normal modes seen following intense quakes) were first observed by accident in the record of a tilt-sensitive instrument designed to study surface physics.…