An Elementary Treatise on Spinning Tops and the Theory of Gyroscopic Motion

1909 ◽  
Vol 5 (81) ◽  
pp. 134
Author(s):  
C. S. Jackson ◽  
H. Crabtree
Keyword(s):  
Gyroscopic Motion

Possibility of Reducing Spar-Type FOWT Hydrodynamic Response Using a Torus Structure With Annular Flow

2021 ◽  
Author(s):  
Motohiko Murai ◽  
Xiaolei Liu
Keyword(s):  
Annular Flow ◽  
Rigid Bodies ◽  
Offshore Wind ◽  
Design Parameters ◽  
Offshore Wind Turbine ◽  
Rotational Axis ◽  
Body Rotation ◽  
Marine Industry ◽  
Hydrodynamic Response ◽  
Gyroscopic Motion

Abstract Gyroscopic motion is considered as an appropriate approach to suppress the shaking motion of rigid bodies. Its spatial orientation is also used to make gyro compasses in the marine industry. In this paper, the floating offshore wind turbine (FOWT) was designed based on potential theory and gyroscopic effect and rotational axis retention effect were also considered, so that FOWT could obtain better hydrodynamic response. However, gyroscopic motion was generated through an annular flow in the internal torus instead of rigid body rotation. The scale of torus and the angular velocity of the annular flow were the design parameters that this article was eager to understand obviously. By vast quantity of calculations, the suitable range of design parameters was obtained.

Dynamic Response of Spinning Blades Subjected to Gyroscopic Motion

1994 ◽  
Vol 116 (1) ◽  
pp. 6-15 ◽  
Author(s):  
T. H. Young ◽  
G. T. Liou
Keyword(s):  
Differential Equations ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Parametric Instability ◽  
Spin Axis ◽  
System Response ◽  
First Order ◽  
System Equations ◽  
Element Technique ◽  
Gyroscopic Motion

This paper presents an investigation into the vibration and stability of a blade spinning with respect to a nonfixed axis. Due to the motion of the spin axis, parametric instability of the blade may occur in certain situations. In this work, the discretized equations of motion are first formulated by the finite element technique. Then the system equations are transformed, by a special modal analysis procedure, into independent sets of first-order simultaneous differential equations. Each set of differential equations is solved analytically by the method of multiple scales if the precessional speed of the spin axis is assumed to be small compared to the spin rate of the blade, yielding the system response and the expressions for the boundaries of the unstable regions. Finally, the effects of system parameters on the changes in these boundaries are studied numerically.

Topics in Gyroscopic Motion

1953 ◽  
Vol 20 (1) ◽  
pp. 1-8
Author(s):  
H. Poritsky
Keyword(s):  
Kinetic Equations ◽  
Spin Axis ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
Gyroscopic Motion

Abstract After a brief review of the fundamental kinetic equations of gyroscope motion, the following topics are considered: (a) The erection of an electrically driven gyroscope when an electrical torque is applied. (b) The effect of inequality of the principal moments of inertia normal to the spin axis, on gyroscope motion. (c) The effect of inertia of the gimbals on motion of the gyroscope.

Motion of a Sphere on a Plane

1994 ◽  
Author(s):  
Yong-Xian Xu ◽  
Dilip Kohli ◽  
Larry Vezina ◽  
Daniel R. Speranza
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Contact Point ◽  
Break Point ◽  
Degree Of Freedom ◽  
Geometric Center ◽  
Inertia Properties ◽  
Gyroscopic Motion ◽  
The Mathematical Model ◽  
First Time

Abstract The motion of a sphere on a plane is a five degree-of-freedom motion. It consists of two independent translations of the geometric center of the sphere and three rotations corresponding to gyroscopic motion of the sphere. The trajectory of an imbalanced sphere on the plane depends on: (1) the physical and inertia properties of the sphere, (2) the initial conditions of motion, and (3) the friction between the sphere and the plane. To predict the trajectory of the sphere, a general Eulerian mathematical model is developed which takes into account these conditions. The mathematical model is verified through experimentation. For the first time, general characteristics of the translatory and rotatory motions of the imbalanced sphere with general inertia distribution are presented. The existence of the “break point” in the trajectory is illustrated by examples. The trajectory (track) of the contact point on the surface of the sphere is also analyzed.

The Null Dynamical Effect, and Some Frequency Spectra, of Resonant Inertial Pressure Waves in a Rapidly Rotating, Right Circular, Sectored Cylinder

1980 ◽  
Vol 47 (3) ◽  
pp. 475-481
Author(s):  
W. E. Scott
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Incompressible Liquid ◽  
Reasonable Agreement ◽  
Center Of Mass ◽  
Experimental Results ◽  
Pressure Waves ◽  
Frequency Spectra ◽  
Gyroscopic Motion ◽  
Amplitude Growth

It is shown that inertial waves in the form of standing asymmetrical pressure waves can exist in an incompressible liquid in a rotating sectored cylinder in a rigid body (e.g., a top or a missile) executing a small amplitude gyroscopic motion about its center of mass. Some of the frequency spectra of these waves are presented along with the result that sectoring the cylinder into any number of equal sectors results in eliminating the destabilizing effect of these waves (i.e., the amplitude growth of the motion of the rigid container) when there is a “Stewartson” resonance between the frequency of one of the inertial modes and the frequency of the nutational component of the motion of the container. Experimental results are in reasonable agreement with the theory.

scholarly journals Gyroscopic motion of superfluid-trapped atomic condensates

2003 ◽  
Vol 36 (9) ◽  
pp. 1703-1718 ◽  
Author(s):  
Halvor M ll Nilsen ◽  
Dermot McPeake ◽  
J F McCann
Keyword(s):  
Atomic Condensates ◽  
Gyroscopic Motion

The Influence of Coriolis Forces on Gyroscopic Motion of Spinning Blades

1983 ◽  
Vol 105 (2) ◽  
pp. 342-347 ◽  
Author(s):  
F. Sisto ◽  
A. Chang ◽  
M. Sutcu
Keyword(s):  
Cantilever Beams ◽  
Coriolis Forces ◽  
Coriolis Acceleration ◽  
Motion Responses ◽  
Gyroscopic Motion ◽  
Forced Excitation

Turbomachine blades on spinning and precessing rotors experience gyroscopically induced instabilities and forcing. With vehicle-mounted turbomachines, either constant or harmonic precession occurs, depending on vehicle or mount motion. Responses of uniform cantilever beams at arbitrary stagger, subjected to the noted rotor motion, are predicted in both self-excited and forced-excitation modes taking into account Coriolis acceleration.

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