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The dynamics of a constrained three-vortex problem, a free point vortex pair in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized…
The purpose of this work is twofold: to present mathematical expressions for the kinematics of an articulated mechanism and to perform numerical experiments with the implemented code. The system of rigid parts is made of two slender bars…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using Molecular Dynamics Simulations, and…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time,…
We describe an experiment dedicated to the study of the trajectories of a ball bouncing randomly on a vibrating plate. The system was originally used, considering a sinusoidal vibration, to illustrate period doubling and the route to chaos.…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
The dynamics of a set of rods bouncing on a vertically vibrated plate is investigated using experiments, simulations, and theoretical analysis. The experiments and simulations are performed within an annulus to impose periodic boundary…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
We study from a statistical physics perspective the dynamics of a bouncing ball maintained in a chaotic regime thanks to collisions with a plate experiencing an aperiodic vibration. We analyze in details the energy exchanges between the…
We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
Autonomous landing on a moving platform presents unique challenges for multirotor vehicles, including the need to accurately localize the platform, fast trajectory planning, and precise/robust control. Previous works studied this problem…
We examine the kinetics of a snowball that is gaining mass while is rolling downhill. This dynamical system combines rotational effects with effects involving the variation of mass. In order to understand the consequences of both effects we…
In this article, a continuous analogue of strictly non-Volterra quadratic dynamical systems with continuous time and points of equilibrium is investigated, a phase portrait of the system is constructed, numerical solutions are found, and a…
This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular…
The averaged dynamics of various two-phase systems in a high-frequency vibration field is studied theoretically. The continuum approach is applied to describe such systems as solid particle suspensions, emulsions, bubbly fluids, when the…
The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of…