Related papers: The Diver with a Rotor
A three-dimensional direct numerical simulation (3D DNS) is performed to describe the turbulent flow in an enclosed rotor-stator cavity characterized by a large aspect ratio $G=(b-a)/h=18.32$ and a small radius ratio $a/b=0.15$ ($a$ and $b$…
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation…
We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…
The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed circular cylindrical shells, regarded as three-dimensional…
Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are…
The current understanding of motility through body shape deformation of microorganisms and the knowledge of fluid flows at the microscale provides ample examples for mimicry and design of soft microrobots. In this work, a two-dimensional…
We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on…
The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models…
The literature on dynamical systems has, for the most part, considered self-oscillators (i.e., systems capable of generating and maintaining a periodic motion at the expense of an external energy source with no corresponding periodicity)…
A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos (1995) and preserves the…
A theoretical expression for the drag on a spherical bubble is derived for the entire range from very viscous to inertial flow conditions. It is based on a solution for only that part of the velocity profile that determines the drag. It is…
Turbines are crucial to our energy infrastructure, and ensuring their bearings function with minimal friction while often supporting heavy loads is vital. Vibrations within a bearing can signal the presence of defects, friction, or…
This work addresses the problem of robust attitude control of quadcopters. First, the mathematical model of the quadcopter is derived considering factors such as nonlinearity, external disturbances, uncertain dynamics and strong coupling.…
Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational response. This response would translate into…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
This paper carries out the mathematical modeling, simulation, and control law design for a quadrotor with variable-pitch propellers. The use of variable-pitch propeller for thrust variation instead of RPM regulation facilitates generation…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…
Classical dynamical equations describing a certain version of the nonHamiltonian interaction of two rotators (Euler tops with completely degenerate inertia tensors) are considered. The simplest case is integrated. It is shown that the…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…