Slow motion of a paraboloid of revolution in a rotating fluid

1958 ◽  
Vol 3 (4) ◽  
pp. 404-410 ◽  
Author(s):  
L. V. K. Viswanadha Sarma
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Radial Displacement ◽  
Direct Consequence ◽  
Slow Motion ◽  
Uniform Motion ◽  
Rotating Fluid ◽  
Body Rotation ◽  
Axis Of Rotation ◽  
Paraboloid Of Revolution

The slow uniform motion, after an impulsive start from relative rest, of a paraboloid of revolution along the axis of a rotating fluid is investigated by using a perturbation method. The principal purpose of the note is to illustrate the mechanism by which the fluid is not subjected to any substantial radial displacement, which is a direct consequence of the requirement that the circulation round material circuits should be constant when the perturbation velocities due to the motion of the paraboloid remain small. It appears that the mechanism is an oscillatory one in which the distance between any fluid particle and the axis of rotation oscillates sinusoidally in time with small amplitude. As time progresses, the amplitude of the oscillation decays to zero everywhere except on the paraboloid. The ultimate motion is then a rigid body rotation everywhere except on the paraboloid and the axis of rotation, where the perturbation velocities continue to oscillate indefinitely with small amplitude.

On the slow motion of a sphere along the axis of a rotating fluid

1952 ◽  
Vol 48 (1) ◽  
pp. 168-177 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Condition ◽  
Angular Velocity ◽  
Relative Velocity ◽  
Steady Motion ◽  
Slow Motion ◽  
Uniform Motion ◽  
Two Dimensional ◽  
Rotating Fluid ◽  
Inviscid Incompressible Fluid ◽  
Axis Of Rotation

We consider the perturbation of the velocity of an inviscid incompressible fluid rotating about an axis with uniform angular velocity Ω, due to the slow uniform motion, after an impulsive start, of a sphere of radius a along the axis with velocity − V. This problem was first considered by Taylor (4), who obtained a family of solutions for the case of steady motion of a sphere along the axis of rotation of the fluid. All the solutions satisfied the boundary condition at the surface of the sphere and also the condition that the relative velocity should vanish at infinity. It was thought possible that the indeterminacy lay in the manner in which the motion was started. However, an experiment carried out in connexion with the problem showed that if V/aΩ was less than about 0·16 a column of liquid of the same diameter as the sphere was apparently pushed along in front of it. This agreed with Proudman's observation (3) that if the perturbation was small and steady it would be two-dimensional, while in Taylor's solutions the relative motion of the fluid was not small. Taylor (5) suggested that three possibilities presented themselves. Either the motion never becomes steady, or it becomes steady but not small, or it becomes steady and two-dimensional. Of these he preferred the latter, which seems to occur in practice.

Forces on bodies moving transversely through a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 577-599 ◽  
Author(s):  
P. J. Mason
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Vertical Axis ◽  
The Body ◽  
Rotating Fluid ◽  
Size And Shape ◽  
Relative Direction ◽  
Axis Of Rotation

Measurements have been made of the net force F acting on a bluff rigid body moving with velocity U (relative to a fluid rotating about a vertical axis with uniform angular velocity Ω) in a plane perpendicular to the axis of rotation. The force F is of magnitude 2ΩρVU, where ρ is the density of the fluid and V is a volume which depends on the size and shape of the body. The relative direction of F and U is found to depend on the quantity \[ {\cal S}\equiv \frac{2\Omega L}{U}\bigg(\frac{h}{D}\bigg), \] where L and h are horizontal and vertical lengths characterizing the object and D is the depth of the fluid in which the object is placed.

Diagnostic Value of Rigid Body Rotation in Noncompaction Cardiomyopathy

2011 ◽  
Vol 24 (5) ◽  
pp. 548-555 ◽  
Author(s):  
Bas M. van Dalen ◽  
Kadir Caliskan ◽  
Osama I.I. Soliman ◽  
Floris Kauer ◽  
Heleen B. van der Zwaan ◽  
...  
Keyword(s):  
Rigid Body ◽  
Diagnostic Value ◽  
Body Rotation ◽  
Rigid Body Rotation ◽  
Noncompaction Cardiomyopathy

Reduction of residual vibrations in a rotating flexible beam with a moving payload mass

1997 ◽  
Vol 211 (1) ◽  
pp. 25-34 ◽  
Author(s):  
S Choura
Keyword(s):  
Rigid Body ◽  
Position Control ◽  
Rate Of Change ◽  
Torque Control ◽  
Flexible Beam ◽  
Control Force ◽  
Axial Motion ◽  
Body Rotation ◽  
Rigid Body Rotation ◽  
Payload Mass

The reduction of residual vibrations for the position control of a flexible rotating beam carrying a payload mass is investigated. The common practice used to find the position control of a flexible multi-link arm is to assign a torque actuator to each joint while the payload mass is kept fixed relative to the end-link during the time of manoeuvre. This paper examines the stability of the system if either the payload is freed accidentally to move along the beam during the time of manoeuvre or is allowed to span the beam in a desired path for control purposes. A candidate Lyapunov function is constructed and its time rate of change is examined. It is shown that the use of a PD (proportional plus derivative) torque control yields a convergence of residual vibration to zero, an attainment of the rigid-body rotation to a prespecified desired angle of manoeuvre and a constant velocity of the payload mass as it moves relative to the beam. For manipulation purposes, an additional control force is added to the moving actuator in order to regulate its axial motion. It is shown that allowing the axial motion of the payload mass in a prescribed manner leads to a considerable reduction of its residual vibrations as compared to the case where the payload mass is fixed to the beam tip during the time of manoeuvre. Stability is also verified through simulations of rigid-body rotation and payload axial motion track prespecified reference trajectories.

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

scholarly journals Rigid-body rotation of an electron cloud in divergent magnetic fields

2013 ◽  
Vol 20 (7) ◽  
pp. 073502 ◽  
Author(s):  
A. Fruchtman ◽  
R. Gueroult ◽  
N. J. Fisch
Keyword(s):  
Magnetic Fields ◽  
Rigid Body ◽  
Electron Cloud ◽  
Body Rotation ◽  
Rigid Body Rotation
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