remotely control through the Internet. Our objective is threefold. We are attempting to provide an educational resource for chaos, demonstrate a new technology, and experiment with a new method of laboratory education. Figure 1 shows the pendulum control panel. As students vary the driving frequency, they can watch the pendulum's motion switch from simple periodic motion to chaotic motion. The ...

The French Academy units of time and length — the second and the meter — are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each semi oscillation, a 'surprising' coincidence that has no physical reason. We shortly review the steps that led to the choice of the meter as the ten millionth part of the...

A simple circuit is designed and used for studying the motion of a simple pendulum. The circuit can be reproduced for purposes of verifications of various circuits taught theoretically at undergraduate levels. As a useful example of instrumentation, the assembled circuit has enabled illustration of Faraday’s law of induction.

For 3D walking control of a biped robot we analyze the dynamics of a three-dimensional inverted pendulum in which motion i s constrained to move along an arbitrarily defined plane. This analysis leads us a simple linear dynamics, the Three-Dimensional Linear Inverted Pendulum Mode (SD-LIPM). Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern genemtion are discus...

A real pendulum with friction will oscillate for a while after a short push, but will eventually come to rest close to a location where is potential energy has a minimum. If the system is closed, i.e. without a source of energy, it will eventually stop moving at a location near a minimum of the potential, no matter what type of friction force acts on the pendulum. This ‘variation principle’ is ...

The French Academy units of time and length — the second and the meter — are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each oscillation, a 'surprising' coincidence that has no physical reason. We shortly review the steps that led to the choice of the meter as the ten millionth part of the quad...

For realtime walking control of a biped robot, we analyze the dynamics of a three-dimensional inverted pendulum whose motions are constrained onto an arbitrarily defined plane. This analysis leads us a simple linear dynamics, the Three-Dimensional Linear Inverted Pendulum Mode (3D-LIPM). Geometric nature of trajectories under the 3D-LIPM is discussed, and an algorithm for walking pattern genera...

This study introduces two types of self-oscillating circuits that are frequently found in power electronics applications. Special effort is made to relate the circuits to the analogous mechanical systems of some important scientific inventions: Galileo’s pendulum clock and Coulomb’s friction model. A little touch of related history and philosophy of science will hopefully encourage curiosity, a...

In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a simple example where the amplitude of limit cycles and the appearance of period-doubling bifurcations are controlled using a method derived from the frequency domain approach. In the second part, bifurcation theory is used to analyze the dynamical...

The purpose of this document is to establish a technical framework to control Krang in its stable balancing state. We will first discuss related work in inverted pendulum-like systems to get acquianted with the literature. Next, we will present a simple inverted pendulum model, analyze the dynamics and simulate it. We will evaluate the effect of different control gains in state feedback control...