A new sine pendulum

A New Robust Four Parameter Sine Fitting Procedure

In this paper a new procedure to perform four parameters sine fitting is presented in a closed form, ready for standardization. This new procedure grants convergence of the algorithm, even in those cases where the traditional techniques tend to converge to local minimums of the error function. This new procedure can also be used to compute the initial values for the traditional four parameters ...

A new swing-up law for the Furuta Pendulum

In this paper the swing-up problem for the Furuta pendulum is solved applying Fradkov’s speed-gradient (SG) method [1, 9] to a dimension 4 model of the system. The new law is compared with the conventional Åström-Furuta strategy, based on a dimension 2 model. A comparative analysis, including simulations and experiments, whereby the advantages and effectiveness of the new law for swinging the p...

A pendulum theoremt

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...

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine

Some New Inequalities of Jordan Type for Sine

The authors find some new inequalities of Jordan type for the sine function. These newly established inequalities are of new form and are applied to deduce some known results.