Related papers: Linearisation of Simple Pendulum
This paper proposes a qualitative analysis to the simple harmonic motion for students who are not mathematically well-prepared. It uses the variation in speed and acceleration to sketch the velocity-time curve. The curve appears to be…
Time series of string tension of a simple pendulum has not yet been a interesting motion information, even nowadays using a force tension sensor can be measured easily. A numerical procedure is presented how to obtain motion of pendulum bob…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
With the right choice of sensor, a `simple' pendulum has great potential as a seismometer with superior low frequency sensitivity.
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
The general classical equation of spin motion is rigorously derived for a particle with electric and magnetic charges and dipole moments in electromagnetic fields. The equation describing the spin motion relative to the momentum direction…
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
Simple scalar field cosmological models are considered describing gravity assisted crossing of the phantom divide line. This crossing or (de)-phantomization characterized by the change of the sign of the kinetic term of the scalar field is…
The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at…
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In this paper, the familiar problems of free-fall motion and simple harmonic motion (SHM) are combined. The novel composite system passes from regular to chaotic behavior for increasing values of energy $E$. This system is a suitable…
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.
A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the…
We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…
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…
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…
We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the…