In this paper we introduce a PDE system which aims at describing the dynamics of a dispersed phase of particles moving into an incompressible perfect fluid, in two space dimensions. The system couples a Vlasov-type equation and an Euler-type equation: the fluid acts on the dispersed phase through a gyroscopic force whereas the latter contributes to the vorticity of the former. First we give a D...

An introductory exploration of the mechanical influence of long-term gyricity or gyroscopic effect on the dynamics of the Earth is presented. Gyricity exists in a deformable, energy-dissipating, and thus rotationally unstable Earth in the form of internal torques, or the rate of change of angular momentum independent of external torques. The kinematics of the internal torques appear compatible ...

This paper presents a novel controller built to exploit the physical behaviour of a simple dynamical system, namely a spinning wheel. The phenomenon of gyroscopic precession causes the instrument to slowly oscillate when it is spun quickly, providing the performer with proprioceptive feedback. Also, due to the mass of the wheel and tire and the resulting rotational inertia, it maintains a relat...

Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called "frame dragging" and is the pr...

This paper deals with sliding mode hyperplane design for a class of linear parameter-varying (LPV) plants, the state-space matrices of which are an affine function of timevarying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertain...

This paper presents a novel controller built to exploit the physical behaviour of a simple dynamic system, namely a spinning wheel. The phenomenon of gyroscopic precession causes the instrument to slowly oscillate when it is spun quickly, providing the performer with proprioceptive feedback. Also, due to the mass of the wheel and tire and the resulting rotational inertia, it maintains a relativ...

Spinning up a Powerball – a hand-held gyroscopic toy or exerciser that exhibits rotor spin-up when applying appropriate torque to its casing – is a fairly easy task for a human but rather complex to perform with a robot. To accomplish the task of spinning up the rotor of the Powerball with a robot, we measured the motion of a human and identified the conditions an individual uses for a successf...

I watched it for some minutes, somewhat in fear, but more in wonder.. .. it seemed massy and heavy, tapering from the edge into a solid and broad structure above. It was appended to a weighty rod of brass, and the whole hissed as it swung through the air. Abstract In this paper we consider the nonlinear control of the Gyroscopic Pendulum, a novel mechanical system consisting of a physical pendu...

We present two methods for calculating resonant frequencies and mode shapes for fluid-structure vibration problems. We model the fluid-structure interaction problem using the #-V-P, finite element technique. This eigenproblem is more complicated than for ordinary structural analyses, as the formulation produces a quadratic eigenproblem (similar to those for gyroscopic systems). We derive proper...

In this paper we generalize the automated multi–level substructuring method to certain classes of nonlinear eigenvalue problems which can be partitioned into an essential linear and positive definite pencil and a small residual. The efficiency of the method is demonstrated by numerical examples modeling damped vibrations of a structure with nonproportional damping, a gyroscopic eigenproblem, an...