Related papers: A new Visual approach to pendulum period determina…
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass…
The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum…
Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on…
In this paper we revisit the construction by which the $SL(2,\mathbb{R})$ symmetry of the Euler equations allows to obtain the simple pendulum from the rigid body. We begin reviewing the original relation found by Holm and Marsden in which,…
A quantitative method is presented for stopping the intrinsic precession of a spherical pendulum due to ellipsoidal motion. Removing this unwanted precession renders the Foucault precession due to the turning of the Earth readily…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the…
Analysis of transit times in exoplanetary systems accurately provides an instantaneous orbital period, $P(t)$, of their member planets. A long-term monitoring of those transiting planetary systems puts limits on the variability of $P(t)$,…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…
We compute in a relativistic way the time-of-arrival and the traversal time through a region of a free particle with spin 1/2. We do this by applying the relativistic extension of the Event-Enhanced Quantum Theory which we have presented in…
We provide an exact infinite power series solution that describes the trajectory of a nonlinear simple pendulum undergoing librating and rotating motion for all time. Although the series coefficients were previously given in [V. Fair\'en,…
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute…
Let $0<a<b<\infty$ be fixed scalars. Assign independently to each edge in the lattice $\mathbb{Z}^2$ the value $a$ with probability $p$ or the value $b$ with probability $1-p$. For all $u,v\in\mathbb{Z}^2$, let $T(u,v)$ denote the first…
Timescales spanning 24 orders of magnitude smaller than one second can be studied experimentally, and each range is packed with different physical phenomena. This rich range of timescales offers a great context for an innovative…
We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation…
Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical…