I. PROBLEM FORMULATION The Furuta pendulum consists of an arm rotating in the horizontal plane and a pendulum attached to the end of the arm moving freely in the vertical plane, see Fig. 1. The equations of motion of the Furuta pendulum, derived from the standard Euler-Lagrange dynamics, are1 (α + β sin θ)φ̈ + γ cos θθ̈ + 2βθ̇φ̇ sin θ cos θ − γθ̇ sin θ = τφ, γ cos θφ̈ + βθ̈ − βφ̇ sin θ cos θ − δ sin θ ...

Student-Friendly Precision Pendulum Germany (latitude 52 N → 981,274) in the early part of this century. With the information provided in this article, students should be able to easily measure the gravitational field strength to a few parts in 10,000, a degree of precision one to two orders of magnitude better than can be achieved with the usual simple pendulum under comparable conditions. The...

This paper is concerned with the reduction of the number of parameters of LPV and quasi LPV models for the synthesis of LPV gain scheduling controllers. The number of parameters is reduced by the principal component analysis of typical scheduling trajectories. This method enables a systematic trade-off between the number of reduced parameters and the desired accuracy. The approach is illustrate...

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...

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...

A 16-year-old Class II female patient was treated without tooth extraction. The upper first molars were distalized by the Pendulum appliance. After six months, the molars tipped significantly to the distal. To correct this side effect, we decided to upright the molars using skeletal anchorage. On each side, a mini-screw was inserted between first and second premolars in the buccal cortical plat...

When designing a controller, the very first step is mathematical modeling of the concerned plant. As we know that during this mathematical modeling several mathematical approximation, uncertainties in the form of system parameter variations, plant nonlinearities and disturbances are involved. Although the conventional PID controller is vastly used controller but it is linear in nature thus it d...

Abstract: In this paper we show that there are applications that transform the movement of a pendulum into movements in R3. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in the case of system of differential equations with delay argument and in the fr...

Abstract In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For first time, a new and exact expression is obtained for the time “t” of swinging of a simple pendulum from the vertical position to an arbitrary angular position “θ”. The time period “T” of such a pendulum is also exactly expressible in terms of hypergeometric functions.