Stability ?in the mean? of forced oscillations of a gyroscopic system acted on by random forces of friction

1973 ◽  
Vol 9 (10) ◽  
pp. 1098-1101
Author(s):  
E. Ya. Gordon
Keyword(s):  
Forced Oscillations ◽  
Gyroscopic System ◽  
Random Forces ◽  
The Mean

Dynamic Characterization of Human Tendons

1994 ◽  
Vol 208 (4) ◽  
pp. 241-248 ◽  
Author(s):  
H Schechtman ◽  
D L Bader
Keyword(s):  
Loss Modulus ◽  
Testing Machine ◽  
Hydraulic Testing ◽  
Static Stress ◽  
Forced Oscillations ◽  
Dynamic Parameters ◽  
Dynamic Characterization ◽  
Cross Sectional ◽  
The Mean

Human tendons were tested in uniaxial tension with the use of specially designed grips and the local measurement of tendon cross-sectional area. The resulting stress-strain relationship was non-linear in form, with the modulus of elasticity initially increasing to a constant value which decreased as the tendon failed. The ultimate tensile strength (UTS) for the extensor digitorum longus and extensor hallucis longus tendons were 99.9 ± 12.2 MPa and 87.1 ± 125 MPa, respectively. Dynamic characterization of those tendon specimens was achieved by the method of forced oscillations using dedicated software on a hydraulic testing machine. Specimens were subjected to cyclic tension-tension loads at frequencies in the physiological range of 1–4 Hz. The sta*** load was set at values corresponding to prescribed levels between 10 and 80 per cent of the calculated UTS. Results suggest that both the dynamic modulus and the storage modulus were non-linearly proportional to the mean static stress level reaching a peak value at 60 per cent UTS, whereas the loss modulus was independent of the mean static stress. All three dynamic parameters were generally independent of frequency. The trends in the dynamic parameters were explained in terms of the loading/unloading response of tendons, as well as the structural organization of their collagen fibres.

Forced Nonlinear Oscillations of an Autoparametric System—Part 2: Chaotic Responses

1983 ◽  
Vol 50 (3) ◽  
pp. 663-668 ◽  
Author(s):  
H. Hatwal ◽  
A. K. Mallik ◽  
A. Ghosh
Keyword(s):  
Statistical Analysis ◽  
Nonlinear Oscillations ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Forced Oscillations ◽  
Mean Square ◽  
Chaotic Oscillations ◽  
System Part ◽  
The Mean ◽  
Two Degree Of Freedom

Chaotic oscillations arising in forced oscillations of a two degree-of-freedom autoparametric system are studied. Statistical analysis of the numerically integrated nonperiodic responses is shown to be a meaningful description of the mean square values and the frequency contents of the responses. Some qualitative experimental results are presented to substantiate the necessity of performing the statistical analysis of the responses even though the system and the input are deterministic.

scholarly journals The response of lake levels to an unsteady wind stress

1973 ◽  
Vol 8 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B.J. Noye
Keyword(s):  
Cross Section ◽  
Wind Stress ◽  
Equations Of Motion ◽  
Longitudinal Axis ◽  
Longitudinal Component ◽  
Forced Oscillations ◽  
Lake Levels ◽  
Time Analysis ◽  
The Mean ◽  
Rectangular Body

This paper presents a theoretical investigation into the forced oscillations produced in an elongated lake by wind stresses varying in time. Analysis of the appropriate hydrodynamical equations of motion, in the absence of friction, and the equation of continuity give an estimate of the response function of the longitudinal component of the wind stress onto water level. Two mathematical models are used, one giving an analytical solution and the other requiring numerical methods for solution. The first model assumes that the lake is a homogeneous rectangular body of water and the second uses the mean depth h(x) and area of cross section A(x), considered as functions of distance x directed along the longitudinal axis of the lake.

scholarly journals Assessment of heterogeneous airway constriction in dogs: a structure-function analysis

2009 ◽  
Vol 106 (2) ◽  
pp. 520-530 ◽  
Author(s):  
David W. Kaczka ◽  
Robert H. Brown ◽  
Wayne Mitzner
Keyword(s):  
Inverse Modeling ◽  
Function Analysis ◽  
Continuous Distribution ◽  
Structural Heterogeneity ◽  
Forced Oscillations ◽  
Computed Tomographic ◽  
Airway Constriction ◽  
Anesthetized Dogs ◽  
The Mean ◽  
System 1

Obstructive lung diseases are often characterized by heterogeneous patterns of bronchoconstriction, although specific relationships between structural heterogeneity and lung function have yet to be established. We measured respiratory input impedance (Zrs) in eight anesthetized dogs using broadband forced oscillations at baseline and during intravenous methacholine (MCh) infusion. We also obtained high-resolution computed tomographic (HRCT) scans in 4 dogs and identified 20–30 individual airway segments in each animal. The Zrs spectra and HRCT images were obtained before and 5 min following a deep inspiration (DI) to 35 cmH2O. Each Zrs spectrum was fitted with two different models of the respiratory system: 1) a lumped airways model consisting of a single airway compartment, and 2) a distributed airways model incorporating a continuous distribution of airway resistances. For the latter, we found that the mean level and spread of airway resistances increased with MCh dose. Whereas a DI had no effect on average airway resistance during MCh infusion, it did increase the level of airway heterogeneity. At baseline and low-to-moderate doses of MCh, the lumped airways model was statistically more appropriate to describe Zrs in the majority of dogs. At the highest doses of MCh, the distributed airways model provided a superior fit in half of the dogs. There was a significant correlation between heterogeneity assessed with inverse modeling and the standard deviation of airway diameters obtained from HRCT. These data demonstrate that increases in airway heterogeneity as assessed with forced oscillations and inverse modeling can be linked to specific structural alterations in airway diameters.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

Sign in / Sign up

Export Citation Format

Share Document