In the present study, numerical solution of time period a Simple Pendulum under magnetic field investigated. The analytical presented for given problem. problem achieved by using two quadrature methods, namely, Simpson’s 3/8 and Boole’s method. simple pendulum with large angle is presented. results have been compared to exact solution. Absolute relative mistakes Matlab program 2013R has created...

The phenomenon of dynamic stabilization of the inverted rigid planar pendulum whose pivot is forced to oscillate at a high frequency in the vertical direction is revisited. This intriguing nonlinear physical system is analyzed in the paper using time-scale separation and averaging. On this basis, a simple and clear physically meaningful explanation of the phenomenon is presented, followed by th...

Nonlinearity is a profound concept in the study of physical systems. The characteristics of seemingly very simple systems may turn out to be extremely intricate and practically unpredictable due to the nonlinearities associated with them. The study of chaos–that essentially has its basis in nonlinear dynamics–begins with the study of such simple systems. The magnetic pendulum can be one such sy...

We investigate experimentally liquid (oil) droplets vibrating over a bath of the same liquid and relate the phenomenon to the well-known effect of the stabilization of an inverted pendulum on a vibrating foundation (a “Kapitza pendulum”). Small fast vibrations can be substituted by an effective “levitation” force. We further discuss this effective stabilizing “spring force”. Besides the inverte...

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

The inverted-pendulum system is a favorite example system and lecture demonstration of students and educators in physics, dynamics, and control. This system is a simple and valuable laboratory representation of an unstable mechanical system. This paper traces the early history of the inverted-pendulum system, and also compares several of the early treatments from the literature between 1960 and...

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

We seek to understand the behavior of a pendulum under parametric excitation coupled with nonlinear absorber. First, reference system without any absorber, i.e., simple pendulum, is analyzed multiple scale method thanks supposed assumptions about excitation. The equilibrium points are calculated, and their stability determined. phase portraits introduced in order better predict system. Then sam...

In this paper a real time control for swing-up stabilization of inverted pendulum is designed using Fuzzy logic. In the model proposed here a single rulebase is used to control both position and angle simultaneously during both swing-up and stabilization. The proposed fuzzy control scheme successfully fulfills the control objectives and also has an excellent stabilizing ability to overcome the ...

Several new types of regular and chaotic behavior of the parametrically driven pendulum are discovered with the help of computer simulations. A simple physical explanation is suggested to the phenomenon of subharmonic resonances. The boundaries of these resonances in the parameter space and the spectral composition of corresponding stationary oscillations are determined theoretically and verifi...