Related papers: The Driven Pendulum at Arbitrary Drive Angle
The dynamics of co- and counter-rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. Starting from linear…
With the right choice of sensor, a `simple' pendulum has great potential as a seismometer with superior low frequency sensitivity.
This paper studies, for a specific oscillatory system composed by a pendulum connected to a seesaw, how the geometry of the different mechanisms of energy introduction conditions the resulting movement, to achieve both a greater amplitude…
An "upward-driven disk" is a novel mechanical device built from LEGO parts. A circular disk is suspended from the point where it is sandwiched between two wheels, making it free to oscillate as a pendulum, but the location of that…
We calculate the torque on an ideal (point) dipole moving with constant velocity through uniform electric and magnetic fields.
We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited…
It is shown that the spin and orbital angular momentum of electric dipole photons have the same operator structure and may differ from each other only by spatial dependence in the very vicinity of the atom. It is shown that the photon twins…
Inspired by Edgar Allan Poe's The Pit and the Pendulum, we investigate a radially driven, lengthening pendulum. We first show that increasing the length of an undriven pendulum at a uniform rate does not amplify the oscillations in a manner…
The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…
We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit…
Angular momentum is taught in every classical mechanics course. It is a difficult topic with misconceptions commonly forming significant barriers to student success. My intention in writing this paper is to combat some of the most common…
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
It is shown that due to Thomas precession, angular momentum is not generally a constant of the motion in a quasiclassical model of the Positronium atom consisting of circular-orbiting point charges with intrinsic spin and associated…
In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two…
The interaction between freely propagating electrons and light waves is typically described using an approximation in which we assume that the electron velocity remains approximately the same during the interaction. In this article we…
A theoretical expression for the drag on a spherical bubble is derived for the entire range from very viscous to inertial flow conditions. It is based on a solution for only that part of the velocity profile that determines the drag. It is…
A state observer design for the inertia wheel pendulum considering static friction of the actuated inertia disc is presented. The frictional force is modeled by the Stribeck effect, with two separate differential equations describing the…
In the paper some regimes of motion of an electric dipole placed in a uniform magnetic field are considered. The motion of both three-dimensional and two-dimensional dipole in the plane perpendicular to the magnetic field is studied. In the…