Galileo, in the XVII century, observed that the small oscillations of a pendulum seem to have constant period. In fact, the Taylor expansion of the period map of the pendulum is constant up to second order in the initial angular velocity around the stable equilibrium. It is well known that, for small oscillations of the pendulum and small intervals of time, the dynamics of the pendulum can be a...

A micro-thrust stand developed by the National Physical Laboratory under ESA funding was calibrated and characterized. The balance is based on the nulled-pendulum principle. The thruster is positioned in a constrained pendulum that is free to move only along the line of thrust. A capacitive displacement sensor measures the movement of the pendulum and is connected via a servo closed loop to a f...

We study dynamics of the inverted pendulum on wheel a soft surface and under proportional-integral-derivative controller. The behaviour such is modelled by system with differential inclusion. If has sensor for rotational velocity pendulum, tilt encoder then this observable. using observed data controller brings stochastic perturbations into system. properties inclusion control studied upper pos...

INTRODUCTION This study compared the dentoalveolar and skeletal effects on Class II malocclusions of the distal jet with concurrent full fixed appliances and the pendulum appliance both followed by fixed appliances. METHODS The 2 samples each consisted of 32 subjects (19 girls and 13 boys) with mean ages at the start of treatment of 12 years 3 months in the distal jet group and 12 years 6 mon...

seistan was one of the important ancient urban centres in south eastern persia. the ruins of the city show the prosperity and fertility of this city to the extent that a british civil officer considered it as the ancient london of asia. this article attempts to describe the enormous latent wealth of this ancient city which made it important for strategic, political and commercial reasons. due t...

Generalised symmetries and point symmetries coincide for systems of first-order ordinary differential equations and are infinite in number. Systems of linear first-order ordinary differential equations possess a generalised rescaling symmetry. For the system of first-order ordinary differential equations corresponding to the time-dependent linear oscillator the invariant of this symmetry has th...

This paper presents the modelling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using Proportional-Integral-Derivative (PID) controller and Linear Quadratic Regulator (LQR). LQR, an optimal control technique, and PID control method, both of which are generally used for control of the linear dynamical systems have been used in this paper to control ...

The “inverted pendulum problem” is perhaps the most widely used benchmarking study to assess the effectiveness of emerging control design techniques. In this paper the “Backpropagation Through Time” learning method is used to train a multilayer perceptron neural network to control an actual physical system, consisting in a pendulum free to pivot on a cart, which is moved by a DC motor within a ...

Manufacturing systems are considered to be dynamical systems in terms of Dynamical Systems Theory. A dynamical model of a flow line is introduced and analysed by using its state space. The work systems of the flow line are compared to a pendulum oscillator, which are driven by the part input and damped by their processing capacity. Depending on the ratio between part input and capacity, the und...

The Inverted Pendulum is one of the most important classical problems of Control Engineering. In this paper, a real-time control for stabilization of inverted pendulum is developed using PID controller. The implementation platform chosen here is FPGA because it exhibits some superior qualities over traditional processors such as parallel processing capability, high sampling rates, flexibility i...