Inclined Large-angle Pendulum May Produce Endless Linear Motion of a Cart When Friction is Negligible

Abstract

We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.

Inertial Propulsion Devices: A Review

“…Since friction causes fast decay in both, some patents have introduced the concept of the pendulum, in which decay is much smaller [119]. A particular patent by the talented inventor Mr. Veljko Milkovic in which an inclined pendulum could offer inertial propulsion to a cart was studied by Allen and Provatidis [120]. The latter study was based on mechanics and computer methods that had been previously developed and documented in [121,122].…”

Inertial Propulsion Devices: A Review

“…Since the friction causes a fast decay in both, there are some patents introducing the concept of the pendulum in which the decay is much smaller [120]. A particular patent of the talented inventor Mr. Veljko Milkovic in which an inclined pendulum could offer inertial propulsion to a cart was studied by Allen and Provatidis [121]. The latter study was based on mechanics and computer methods that had been previously developed and documented in [122,123].…”