Related papers: A computer controlled pendulum with position reado…
With the right choice of sensor, a `simple' pendulum has great potential as a seismometer with superior low frequency sensitivity.
Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control…
We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase…
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has…
This paper investigates the possibility of the motion control of a ball with a pendulum mechanism with non-holonomic constraints using gaits - the simplest motions such as acceleration and deceleration during the motion in a straight line,…
This paper aims to show how to guide students with a familiar example to extract as much physics as possible before jumping into mathematical calculation. The period for a physical pendulum made up of a uniform rod is changed by attaching a…
We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the…
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…
Recently researchers at the University of Illinois coupled a real pendulum to its virtual counterpart. They observed that the two pendulums suddenly start to move in synchrony if their lengths are sufficiently close. In this synchronized…
This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second…
This paper is devoted to a detailed investigation of the perturbed pendulum-like motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are…
We analyze the dynamics of a driven, damped pendulum as used in mechanical clocks. We derive equations for the amplitude and phase of the oscillation, on time scales longer than the pendulum period. The equations are first order ODEs and…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
We present Pendulum Tracker, a computer vision-based application that enables real-time measurement of the oscillatory motion of a physical pendulum. Integrated into the educational platform SimuF\'isica, the system uses the OpenCV.js…
Complex environments, processes and systems may exhibit several distinct modes of physical behaviour or operation. Thus, for example, in their design, a set of mathematical models may be needed, each model having its own domain of…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
A compound pendulum of simple geometry was built from a lightweight rod to which a pair of masses are clamped, one above and the other below the axis of rotation. By making the position of the upper mass variable, it was found that the…
The inverted pendulum is a non-linear unbalanced system that needs to be controlled using motors to achieve stability and equilibrium. The inverted pendulum is constructed with Lego and using the Lego Mindstorm NXT, which is a programmable…
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…