The approximation of a humanoid robot by an inverted pendulum is one of the most frequently used models to generate a stable walking pattern using a planned zero moment point (ZMP) trajectory. However, on account of the difference between the multibody model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot fall...

Neurons as active unities are connected one with the others by synapses in an electronic way. Each neuron as N port electronic medium scatters input waves and transmits output waves to other neurons. By voltage waves each neuron interacts with the others in a complex way. Scattering processes create dependence among neurons. We show that a multi pendulum mechanical system can be a simple model ...

Stephenson (1908a, b) showed that it is possible to stabilize a single rigid pendulum in its inverted, or upside-down, equilibrium position by subjecting the pivot to small vertical oscillations of suitably high frequency. He confirmed his theoretical predictions by a practical demonstration of the phenomenon. While this is a well-known curiosity of classical mechanics it does not seem to be ge...

The seismoscope is a simple instrument designed originally to give a largely qualitative indication of the strong ground motions produced by an earthquake. It consists of a smoked watch glass attached to a two-degree-of-freedom pendulum with a period of 1⁄4 sec and damping about 10 per cent of critical; a pen records the pendulum motions on the watch glass. One point on the displacement spectru...

The approximation of humanoid robot by an inverted pendulum is one of the most used models to generate a stable walking patterns using a planned Zero Moment Point (ZMP) trajectory. However, on account of the difference between the multi-body model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot falls down. To ...

In this paper we investigate the stability and the onset of chaotic oscillations around the pointing-up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions. The driven control torque is defined as a proportional plus integral plus derivative (PID) control of the deviation angle with respect to the point...

We expand the anecdotic report by Johansson that back-and-forth linear harmonic motions appear uniform. Six experiments explore the role of shape and spatial orientation of the trajectory of a point-light target in the perceptual judgment of uniform motion. In Experiment 1, the target oscillated back-and-forth along a circular arc around an invisible pivot. The imaginary segment from the pivot ...

In this paper, we study a simple passive dynamic biped robot with point feet and legs without knee. The mathematical model describing the robot is a switched system, which includes an inverted double pendulum. Robot’s gait and its stability depend on parameters such as the slope of the ramp, mass distribution for the robot, and the length of its legs. The main result of the paper is an asymptot...

We investigate the dynamics of an inverted pendulum subjected to Jacobi elliptic forcing both numerically and experimentally. In so doing, we hope to provide a coherent picture on stability of an inverted pendulum subjected to forcing that ranges from harmonic to nonharmonic in nature. We are able to determine the regions of stability of a sinusoidally forced inverted pendulum, with results sim...

The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of automatic control. In this paper two Neural Network controllers to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state are described. Both controllers are able to learn the demonstrated behavior which was swinging u...