Angular Momentum of a Torque-Free Deforming Axisymmetric Gyro

1994 ◽  
Vol 61 (1) ◽  
pp. 117-123
Author(s):  
F. P. J. Rimrott ◽  
F. Janabi-Sharifi
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Large Deformation ◽  
Small Deformation ◽  
Matrix Form ◽  
Stability Studies ◽  
Attitude Stability ◽  
Small Deformations

Attitude drift and attitude stability studies of torque-free gyros involve an angular momentum that is constant in magnitude and direction. The problem is to find suitable coordinates to describe the gyro’s behavior, and then to express the (constant) angular momentum in these coordinates. Expressions for small deformation are available. In the present paper the expression, in floating coordinates, for the angular momentum of a torque-free deforming axisymmetric gyro in terms of inertia moments and angular velocity components is extended to beyond small deformations. The angular momentum expression is written first in its general form. Thqn the angular momentum is expressed in matrix form for the calculation of angular momentum components for arbitrarily large deformation. Finally, three models are presented to illustrate the application of the angular momentum expression obtained.

Mechanical properties of the tadpole tail fin

1998 ◽  
Vol 201 (19) ◽  
pp. 2691-2699 ◽  
Author(s):  
PA Doherty ◽  
RJ Wassersug ◽  
JM Lee
Keyword(s):  
Stress Relaxation ◽  
Large Deformation ◽  
Forced Vibration ◽  
Viscoelastic Properties ◽  
Developmental Plasticity ◽  
Rana Catesbeiana ◽  
Small Deformation ◽  
Collagen Fibres ◽  
Tadpole Tail ◽  
Undulatory Swimming

The tadpole tail fin is a simple double layer of skin overlying loose connective tissue. Collagen fibres in the fin are oriented at approximately +/-45 degrees from the long axis of the tail. Three tests were conducted on samples of the dorsal tail fin from 6-10 Rana catesbeiana tadpoles to establish the fin's viscoelastic properties under (1) large-deformation cyclic loading at 1 and 3 Hz, (2) small-deformation forced vibration at 1 and 3 Hz, and (3) stress relaxation under a 0.1 s loading time. The fin was very fragile, failing easily under tensile loads less than 7 g. It was also strikingly viscoelastic, as demonstrated by 72+/-1 % hysteresis loss (at 3 Hz), 16+/-3 % stress remaining after 100 s of stress relaxation and a phase angle of 18+/-1 degrees in forced vibration. As a consequence of its viscoelastic properties, the fin was three times stiffer in small than in large deformation. This may account for the ability of the fin to stay upright during normal undulatory swimming, despite the absence of any skeletal support. Tadpoles in nature are often found with damaged tails. We suggest that the unusually viscoelastic and fragile nature of the fin helps tadpoles escape the grasp of predators. Because the fin deforms viscoelastically and tears easily, tadpoles can escape predators and survive otherwise lethal attacks with only minor lacerations to the fin. Recent studies have shown that certain tadpoles develop taller fins in the presence of predators. This developmental plasticity is consistent with the tail fin acting as a protective but expendable 'wrap' around the core muscle tissue.

Test of Strain-Time Correspondence Principle with Gel-Containing Elastomers

1986 ◽  
Vol 59 (2) ◽  
pp. 305-314 ◽  
Author(s):  
N. Nakajima ◽  
E. R. Harrell
Keyword(s):  
Large Deformation ◽  
Correspondence Principle ◽  
Small Deformation ◽  
Complex Viscosity ◽  
Shear Stresses ◽  
Growth Data ◽  
Stress Growth ◽  
Linear Viscoelastic ◽  
The Difference ◽  
Linear Viscoelastic Theory

Abstract With four NBR samples and one EPR, oscillatory measurements and stress-growth measurements were performed, the former being at very small deformation and the latter leading to large deformation. The Rheometrics mechanical spectrometer was used with a cone-plate fixture. The temperature was 100°C. The stress-growth data of NBR's, converted to complex viscosity-frequency data through the application of stress-time correspondence principle, were in good agreement with those observed in the oscillatory measurement. Thus, the stress-growth data including the large deformation were “linearized” to form a master curve. With the EPR sample, such a linearization was not necessary. The stress-growth data were adequately treated with the linear viscoelastic theory up to shear stresses approaching the steady state. The difference in behavior between the NBR's and EPR is caused by differences in type and extent of long branching and gel present in the samples.

scholarly journals On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

2020 ◽  
Vol 15 ◽  
pp. 9-14
Author(s):  
Sergey G. Fedosin
Keyword(s):  
Angular Momentum ◽  
Neutron Star ◽  
Angular Velocity ◽  
Mass Density ◽  
Nonlinear Function ◽  
Kerr Black Hole ◽  
Special Theory ◽  
Spherical Body ◽  
Theory Of Relativity ◽  
Speed Of Light

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

Why only a small fraction of quasars are radio loud?

2018 ◽  
Vol 14 (S342) ◽  
pp. 201-204
Author(s):  
Xinwu Cao
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Strong Magnetic Field ◽  
Weak Magnetic Field ◽  
Thin Disk ◽  
Relativistic Jets ◽  
Jet Formation ◽  
The Magnetic Field

AbstractIt is still a mystery why only a small fraction of quasars contain relativistic jets. A strong magnetic field is a necessary ingredient for jet formation. Gas falls from the Bondi radius RB nearly freely to the circularization radius Rc, and a thin accretion disk is formed within Rc We suggest that the external weak magnetic field threading interstellar medium is substantially enhanced in this region, and the magnetic field at Rc can be sufficiently strong to drive outflows from the disk if the angular velocity of the gas is low at RB. In this case, the magnetic field is efficiently dragged in the disk, because most angular momentum of the disk is removed by the outflows that lead to a significantly high radial velocity. The strong magnetic field formed in this way may accelerate jets in the region near the black hole, either by the Blandford-Payne or/and Blandford-Znajek mechanisms. If the angular velocity of the circumnuclear gas is low, the field advection in the thin disk is inefficient, and it will appear as a radio-quiet (RQ) quasar.

scholarly journals Binary Orbit Perturbations and the Rotational Angular Momentum of Stellar Interiors

1970 ◽  
Vol 4 ◽  
pp. 187-192
Author(s):  
Stanley Sobieski
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Significant Variation ◽  
Eclipsing Binaries ◽  
Model Parameters ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Stellar Interiors ◽  
Binary Orbit ◽  
Photometric Variation

AbstractCalculations show that a significant variation in the minima of eclipsing binaries should arise for systems where axial precession exists. Several different angular velocity distributions are assumed in order to estimate the expected photometric variation as a function of the model parameters. It is found that the solid body rotation approximation is a reasonable representation unless interiors rotate more rapidly than present models predict.

On the relation between angular momentum and angular velocity

2007 ◽  
Vol 75 (1) ◽  
pp. 53-55 ◽  
Author(s):  
J. P. Silva ◽  
J. M. Tavares
Keyword(s):  
Angular Momentum ◽  
Angular Velocity

scholarly journals Equivalent substitution criteria of aluminum for steel and its application in automobile structures

2020 ◽  
Vol 12 (3) ◽  
pp. 168781402091122
Author(s):  
Song Li ◽  
Jiantao Bai ◽  
Xinchen Wang ◽  
Limin Song ◽  
Kai Luo ◽  
...  
Keyword(s):  
Large Deformation ◽  
Small Deformation ◽  
High Strength ◽  
Steel Tube ◽  
Equal Mass ◽  
Body Structure ◽  
Cross Sectional ◽  
Hollow Section ◽  
Automobile Body ◽  
Triple Cell

Lightweight automobile body structure, made of aluminum, can extend the endurance mileage of electric automobile. However, the mechanisms for the application of aluminum in automobile body structure are not clear until now. The main contribution of this work is to propose a method of equivalent substitution criteria of aluminum for steel. This method researches small deformation and large deformation under bending mode. First, formulations of cross-sectional properties, including open, single-cell, double-cell, three-cell, and four-cell sections, are derived, and equivalent substitution criteria in the case of small deformation, which include equal stiffness design and equal strength design, are initially proposed. Second, in the case of large deformation, the steel circular tube and channel tube are substituted by aluminum tube under equivalent stiffness. The bending resistance of five types of tubes, including rectangular hollow section, rectangular hollow section with double-cell, rectangular hollow section with triple-cell, mild steel, and high-strength steel tube, are, respectively, compared considering crashworthiness under equal mass. Third, the side frame and chassis frame examples verify the effectiveness of the proposed method, which is universal and can also be applied in aerospace structures.

scholarly journals Geodesics in the field of a rotating deformed gravitational source

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641006 ◽  
Author(s):  
K. A. Boshkayev ◽  
H. Quevedo ◽  
M. S. Abutalip ◽  
Zh. A. Kalymova ◽  
Sh. S. Suleymanova
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Angular Velocity ◽  
Circular Orbits ◽  
Frame Dragging ◽  
Test Particles ◽  
Gravitational Source ◽  
Massive Particles ◽  
Analytic Expressions

We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.

Sign in / Sign up

Export Citation Format

Share Document