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...

Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney’s umbrellas when non-conservative positional forces are addit...

Abstract This paper presents, for the first time, an analytical formulation to determine transient response of elastic beam possessing distributed inertia and connected a coupling inertial resonator, represented by gyroscopic spinner. The latter couples transverse displacement components in two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is pre...

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...

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...

2.1 Principles of Inertial Sensors A coordinate system must be defined prior to deployment of an inertial sensor for body motion measurement. If the origin of a moving coordinate system has acceleration (A0) and rotates with a gyroscopic angular velocity (ω), and if a mass (m) has the position vector (r0) and the velocity (u0) with respect to the moving coordinate system, then the inertial forc...

This paper focuses on a model order reduction (MOR) for large-scale rotordynamic systems by using finite element discretization. Typical rotor-bearing systems consist of a rotor, built-on parts, and a support system. These systems require careful consideration in their dynamic analysis modeling because they include unsymmetrical stiffness, localized nonproportional damping, and frequency-depend...

Within the general axially nonadiabatic channel approach described in Paper I of this series [M. Auzinsh, E. I. Dashevskaya, I. Litvin, E. E. Nikitin, and J. Troe, J. Chem. Phys. 139, 084311 (2013)], the present article analyzes the simultaneous manifestation of electrostatic and gyroscopic interactions in the quantum capture of dipolar polarizable symmetric top molecules by ions. As a demonstr...

Micro air vehicles have emerged as a popular option for diverse robotic and teleoperated applications in both open terrain and urban environments because of their inherent stealth and portability. To perform many of the tasks envisioned for micro air vehicles, agility is essential. To date, research efforts to improve agility have focused primarily on constructing complex controllers to enable ...