Related papers: The Upward-Driven Disk, a Steadily Forced Chaotic …
Many damped mechanical systems oscillate with increasing frequency as the amplitude decreases. One popular example is Euler's Disk, where the point of contact rotates with increasing rapidity as the energy is dissipated. We study a simple…
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive, and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and…
Reconfigurable robots are at the forefront of robotics innovation due to their unmatched versatility and adaptability in addressing various tasks through collaborative operations. This paper explores the design and implementation of a novel…
This paper presents a novel type of mobile rolling robot designed as a modular platform for non-prehensile manipulation, highlighting the associated control challenges in achieving balancing control of the robotic system. The developed…
The nature of an instability that controls the transition from static to dynamical friction is studied in the the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit…
The inverted pendulum is a non-linear unbalanced system that needs to be controlled using motors to achieve stability and equilibrium. The inverted pendulum is constructed with Lego and using the Lego Mindstorm NXT, which is a programmable…
It is shown that vibrated packings of frictional disks self-organize cooperatively onto a rotational-transport state where the long-time angular velocity $\bar\omega_i$ of each disk $i$ is nonzero. Steady rotation is mediated by the…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
Spinning ice discs in nature have been reported for more than a century, yet laboratory experiments have yielded diverse observations and contradictory explanations, leaving the mechanism behind the disc motion elusive. Here we combine…
The Foucault Pendulum is a Spherical Pendulum of fixed length with two angular degrees of freedom, attached to a suspension which rotates once a day around the Earth axis at a distance essentially set by Earth radius and the geodetic…
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
In the paper we study the existence of a forced oscillation in two Lagrange systems with gyroscopic forces: a spherical pendulum in a magnetic field and a point on a rotating closed convex surface. We show how it is possible to prove the…
The fluid-structure interaction between a thin circular disk and its turbulent wake is investigated experimentally and described with a low-order stochastic model. The disk faces a uniform flow at Reynolds number Re=133 000 and can rotate…
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between…
We numerically examine the dynamic phases and pattern formation of two-dimensional monodisperse repulsive disks driven over random quenched disorder. We show that there is a series of distinct dynamic regimes as a function of increasing…
The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we…
I present a chaotic pendulum based on the repulsive force between a random array of point sources of air flow and the conical tip of a rigid pendulum. Source code is provided for generation of random aperture arrays. The chaotic motion was…