Abstract: In this paper we show that there are applications that transform the movement of a pendulum into movements in R3. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in the case of system of differential equations with delay argument and in the fr...

Abstract In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For first time, a new and exact expression is obtained for the time “t” of swinging of a simple pendulum from the vertical position to an arbitrary angular position “θ”. The time period “T” of such a pendulum is also exactly expressible in terms of hypergeometric functions.

This paper presents an earthing resistance tester that uses resonant circuit technology to operate with a simple earthing electrode and without auxiliary electrodes. The measurement mechanism is analyzed using an earth return circuit model. The earthing electrode being tested, a lead wire, a return wire and the soil itself comprise the earth return circuit (LRC serial circuit). The requirements...

We consider the double mathematical pendulum in the limit when the ratio of pendulum masses is close to zero and the ratio of pendulum lengths is close to infinity. We found that the limit system has a hyperbolic periodic trajectory, whose invariant manifolds intersect transversally and the intersections are exponentially small. In this case we obtain an asymptotic formula of the homoclinic inv...

Anodic bonding was used to fabricate a 10 mm diameter × 640 nm tall annular geometry suitable for torsion pendulum studies of confined 3He. For pure 3He at saturated vapor pressure the inertia of the confined fluid was seen to be only partially coupled to the pendulum at 160 mK. Below 100 mK the liquid’s inertial contribution was negligible, indicating a complete decoupling of the 3He from the ...