Periodic motion involving a swinging pendulum was studied. As the pendulum oscillated, its motion was captured using video and computer technology. When analyzed, the period of the motion was found to be given by two multiplied by Pi multiplied by the square root of the quantity of the pendulum’s length divided by the acceleration due to gravity. Therefore, the period, or time to complete a ful...

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

In this note we will derive the equations of motion for a compound pendulum being driven by external motion at the center of rotation. A compound pendulum is a pendulum consisting of a single rigid body rotating around a fixed axis. In contrast to the simple pendulum we studied in class, a compound pendulum can have an arbitrary distribution of mass, which means that it better models real-world...

The double pendulum is a classic dynamical system, capable of chaotic behavior in a four-dimensional phase space. The driven case introduces even more peculiar behaviors and opens the possibility for stable folded modes. In this paper, we explore the double pendulum in both driven and undriven cases through experimental observation and simulations, focusing on time-to-flip as a major measure of...

The agreement between the intrinsic damping, obtained from the sustained oscillations measurements, and the values measured directly in forced oscillations has been verified. Therefore, it is possible to measure directly the intrinsic damping from forced oscillations, without additional calculations and with minor effort. At the same time the damping behaviour measured by different modes with a...

Consider a double pendulum under the external force. This model can be described by the multi-speed systems of ordinary differential equations. We study the existence of stable motions depending on the parameters of the system and on the value of the external force. Critical values of the parameters are defined. Ключевые слова: slow-fast systems; delayed loss of stability; double pendulum

We present a method for determining the uncertainty in the measurement of parameters that describe the dynamics of a Foucault's pendulum. In the document, we review how these parameters can be obtained. Then, we propose a method for evaluating the uncertainty in their determination. We illustrate the method with experimentation made on a 28m height pendulum located at 20° 35' north latitude.

The hybrid solution to the pendulum swinging-up and stabilizing problem introduced by Åström and Furuta is based in two steps: an energy injection and a linear stabilization around the desired inverted position. However the energy injection stage only considers the pendulum, and not the motion of the pivot. Furthermore, for the stabilization stage linear law, only a very small basin of attracti...

In this article we discuss the primliminary results of stabilising a vertically driven pendulum. Following the brief introduction on the importance of this ‘toy’ problem, we give an account of the experimental set up. We then explain the parameter extraction from the experimental data which form a cucial part of our quantitative study. We also find the stability boundary for a small range of dr...

Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions. ! 1999 Elsevier Science Ltd. All righ...