scholarly journals III. Researches in physical astronomy

1831 ◽  
Vol 121 ◽  
pp. 17-66
Keyword(s):  
Angular Velocity ◽  
Major Axis ◽  
The Body ◽  
Fixed Plane ◽  
Resisting Medium ◽  
Axis Of Rotation ◽  
Geographical Latitude ◽  
The Mean ◽  
The Stability ◽  
Revolving Body

In last April I had the honour of presenting to the Society a paper containing expressions for the variations of the elliptic constants in the theory of the motions of the planets. The stability of the solar system is established by means of these expressions, if the planets move in a space absolutely devoid of any resistance*, for it results from their form that however far the ap­proximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain only periodic inequalities, each of the three other constants, namely, the longitude of the node, the longitude of the perihelion, and the longitude of the epoch, contains a term which varies with the time, and hence the line of apsides and the line of nodes revolve continually in space. The stability of the system may therefore be inferred, which would not be the case if the eccentricity, the major axis, or the tangent of the inclination of the orbit to a fixed plane contained a term varying with the time, however slowly. The problem of the precession of the equinoxes admits of a similar solution; of the six constants which determine the position of the revolving body, and the axis of instantaneous rotation at any moment, three have only periodic inequalities, while each of the other three has a term which varies with the time. From the manner in which these constants enter into the results, the equilibrium of the system may be inferred to be stable, as in the former case. Of the constants in the latter problem, the mean angular velocity of rotation may be considered analogous to the mean motion of a planet, or its major axis ; the geographical longitude, and the cosine of the geographical latitude of the pole of the axis of instantaneous rotation, to the longitude of the perihelion and the eccentricity; the longitude of the first point of Aries and the obliquity of the ecliptic, to the longitude of the node and the inclination of the orbit to a fixed plane; and the longitude of a given line in the body revolving, passing through its centre of gravity, to the longitude of the epoch. By the stability of the system I mean that the pole of the axis of rotation has always nearly the same geographical latitude, and that the angular velocity of rotation, and the obliquity of the ecliptic vary within small limits, and periodically. These questions are considered in the paper I now have the honour of submitting to the Society. It remains to investigate the effect which is produced by the action of a resisting medium; in this case the latitude of the pole of the axis of rotation, the obliquity of the ecliptic, and the angular velocity of rotation might vary considerably, although slowly, and the climates undergo a con­siderable change.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 15-16
Keyword(s):  
Angular Velocity ◽  
The Other ◽  
Similar Solution ◽  
Axis Of Rotation ◽  
Geographical Latitude ◽  
The Law ◽  
The Stability ◽  
Revolving Body ◽  
Analytical Expressions

The author has shown in a former paper, published in the last part of the Philosophical Transactions for 1830, that the stability of a system of bodies subject to the law of gravitation, is always preserved, provided they move in a space absolutely devoid of resistance. This conclusion results from the analytical expressions for the variations of the elliptic constants in the theory of the Planetary Motions. In the present paper he extends his researches to the problem of the precession of the Equinoxes, which admits of a similar solution to the former. Of the six constants which determine the position of the revolving body, and the axis of instantaneous rotation, at any instant, three have only periodic inequalities; while the other three have each a term which varies as the time; but from the manner in which these constants enter into the resulting expressions, the equilibrium of the system may be inferred to be stable, as in the former case. By the stability of the system, the author wishes to be understood to mean that the pole of the axis of rotation has always nearly the same geographical latitude, and that the angular velocity of rotation, and the obliquity of the ecliptic vary within small limits; and that its variation is periodical.

scholarly journals XXII. Researches in physical astronomy

1830 ◽  
Vol 120 ◽  
pp. 327-357
Keyword(s):  
Planetary System ◽  
Major Axis ◽  
Disturbing Function ◽  
Disturbing Force ◽  
Eccentric Anomaly ◽  
Fixed Plane ◽  
Resisting Medium ◽  
Independent Variable ◽  
Law Of Attraction ◽  
The Stability

In the first volume of the Mécanique Céleste, Laplace has given expressions for the variations of the elliptic constants, which are true when the square and higher powers of the disturbing force are neglected; and he has proved, upon the supposition that the planets move in the same direction, in orbits nearly circular and little inclined one to another, that the eccentricities and inclinations vary within small limits, thereby demonstrating within these conditions the stability of the planetary system. But these conditions are not necessary to the stability of a system of bodies, subject to the law of attraction, which obtains in our system. I have given in the following investigation the expres­sions for the variations of the elliptic constants, which are rigorously true whatever power of the disturbing force be retained; and it is easy to con­clude from the form of their expressions, that however far the approximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain no term which varies with the time; their variations are all periodic, and they oscillate therefore within certain limits. This theorem is no longer true if the planet moves in a resisting medium. I have also given some equations which obtain when an angle is taken for the independent variable, which in the elliptic movement is the eccentric anomaly, which are of remarkable simplicity, and which, as far as I know, have never been noticed, and the development of the disturbing function R to the quantities involving the squares and products of the eccentricities inclusive.

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.

scholarly journals Simulation of Motion Stability of Deformed Elongated Bodies Based on Variations of Angular Velocities in Roll

2019 ◽  
Vol 18 (3) ◽  
pp. 646-677
Author(s):  
Irina Romanova
Keyword(s):  
Angular Velocity ◽  
Body Movement ◽  
Stability Boundary ◽  
Complex Form ◽  
Passive Movement ◽  
The Body ◽  
Slip Angle ◽  
Motion Stability ◽  
Angular Velocities ◽  
The Stability

The class of moving objects, which are bodies of revolution, which for some reason have undergone irreversible deformations of the hull, is considered. The immediacy of the problem being studied has to do both with the need to study the dynamics of such objects and the insufficiency of the studies already conducted, which are mainly focused on the study of the effects of aeroelasticity or mass asymmetry and do not affect the dynamics of bodies with irreversible deformations. The problem of the motion stability of the considered objects, including the process of interaction of the longitudinal and lateral movements of the deformed body, is formulated. Particular attention is paid to the movement of the curved body with rotation about the roll and the identification of the presence of critical roll velocities. It is noted that for the case of passive movement there are three possible reasons for this interaction: aerodynamic, kinematic, inertial. A theoretical approach has been developed that takes into account the specific features of the geometry of deformed bodies. The approach made it possible in practical studies to determine the allowable deformation levels and its relationship with the motion parameters of deformed bodies. The stability analysis was carried out based on the stability criteria of the system solutions describing the body movement according to the Routh – Hurwitz criterion. The body parameters , which have a varying degree of influence on the stability of movement, are determined. In a more general case, the curve of the stability boundary for a given angular velocity in roll will have a more complex form than a simple hyperbola. The possibility of obtaining a direct solution to a nonlinear to the determining parameters equation is also shown. It will make it possible to obtain the dependences of the critical heel velocities and stability ranges on these parameters. Mathematical modeling based on the developed techniques, carried out for direct and curved bodies, showed that the body curvature has a significant effect on the displacement of the lines of derivative pitch moments in the angle of attack and the moment of sliding in the angle of slip relative to the limits of stability. The range of angular velocities for the roll is determined, in which a loss of stability is observed for the curved body. The effect of variations in the angular velocity and the relative change in the derivative of the yaw moment coefficient in the slip angle on the value of the determining factor from the stability conditions for the direct and curved bodies is analyzed. It is shown how the curvature of the body leads to a shift of the saddle point. The effect of a change in the Mach number on the determining coefficient of characteristic equations is analyzed.

A study of motions in a rotating liquid

1951 ◽  
Vol 206 (1084) ◽  
pp. 108-130 ◽  
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Forced Oscillations ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Small Motion ◽  
Axis Of Rotation ◽  
Rotating Liquid

Starting with the equations of motion for a perfect, incompressible fluid referred to a coordinate system which rotates about a vertical axis with uniform angular velocity R , the physical condition of ‘small motion’ is determined which permits the equations to be linearized. The small motions resulting from forced oscillations of a rotating liquid are investigated. It is shown that there are three types of flow depending on the relative magnitudes of the impressed frequency β and the angular velocity R of the fluid. Two of the regimes are studied in detail. A similarity law is developed which gives the solution of a class of problems of oscillations for β > 2 R in terms of the solutions to similar irrotational problems. An attempt is made to explain how slow, two-dimensional motion can be produced by introducing a boundary condition which is three-dimensional (as observed in experiments performed by G. I. Taylor), by considering problems from the moment at which the disturbance is created from rest relative to the rotating system, with the only initial assumption that the fluid is rotating uniformly like a solid body. For the particular cases studied the results are in agreement with Taylor’s experiments, in that the flow is found to become steady and two-dimensional if the disturbance which causes it approaches a steady state. If the disturbance is due to a body which moves along the axis of rotation of the fluid, the steady two-dimensional behaviour may be expected everywhere except in the neighbourhood of the surface of an infinite cylinder which encloses the body and whose generators are parallel to the axis of rotation. To resolve an apparent disagreement between certain theoretical results by Grace on the one hand, and experimental evidence by Taylor and the author’s conclusions, on the other, arguments are advanced that the various results may be in agreement, provided Grace’s are given a new interpretation.

scholarly journals A letter to Sir John W. Lubbock, Bart., F. R. S. &c., On the stability of the Earth’s axis of rotation

1854 ◽  
Vol 6 ◽  
pp. 151-152
Keyword(s):  
Geological Society ◽  
Resisting Medium ◽  
Axis Of Rotation ◽  
The Earth ◽  
The Stability ◽  
Earth’S Interior ◽  
Earth's Interior

The author refers to a communication to the Geological Society by Sir John Lubbock, in which he appeals, in support of the possibility of a change in the earth’s axis, to the influence of two disturbing causes, which appear to have almost entirely escaped the notice of Laplace and Poisson in their investigations on the stability of the earth’s axis of rotation:—1. The necessary displacement of the earth’s interior strata arising from chemical and physical actions during the process of solidification. 2. The friction of the resisting medium in which the earth is supposed to move.

scholarly journals Moving and fixed axoids of frenet thrihedral of directing curve on example of cylindrical line

2020 ◽  
Vol 11 (3) ◽  
pp. 41-48
Author(s):  
T. A. Kresan ◽  
◽  
S. F. Pylypaka ◽  
V. M. Babka ◽  
Ya. S. Kremets ◽  
...  
Keyword(s):  
Angular Velocity ◽  
Solid Body ◽  
Rotational Motion ◽  
Linear Velocity ◽  
The Body ◽  
Helical Line ◽  
Spatial Motion ◽  
Instantaneous Axis Of Rotation ◽  
Axis Of Rotation ◽  
Curvature And Torsion

If the solid body makes a spatial motion, then at any point in time this motion can be decomposed into rotational at angular velocity and translational at linear velocity. The direction of the axis of rotation and the magnitude of the angular velocity, that is the vector of rotational motion at a given time does not change regardless of the point of the solid body (pole), relative to which the decomposition of velocities. For linear velocity translational motion is the opposite: the magnitude and direction of the vector depend on the choice of the pole. In a solid body, you can find a point, that is, a pole with respect to which both vectors of rotational and translational motions have the same direction. The common line given by these two vectors is called the instantaneous axis of rotation and sliding, or the kinematic screw. It is characterized by the direction and parameter - the ratio of linear and angular velocity. If the linear velocity is zero and the angular velocity is not, then at this point in time the body performs only rotational motion. If it is the other way around, then the body moves in translational manner without rotating motion. The accompanying trihedral moves along the directing curve, it makes a spatial motion, that is, at any given time it is possible to find the position of the axis of the kinematic screw. Its location in the trihedral, as in a solid body, is well defined and depends entirely on the differential characteristics of the curve at the point of location of the trihedral – its curvature and torsion. Since, in the general case, the curvature and torsion change as the trihedral moves along the curve, then the position of the axis of the kinematic screw will also change. Multitude of these positions form a linear surface - an axoid. At the same time distinguish the fixed axoid relative to the fixed coordinate system, and the moving - which is formed in the system of the trihedral and moves with it. The shape of the moving and fixed axoids depends on the curve. The curve itself can be reproduced by rolling a moving axoid over a fixed one, while sliding along a common touch line at a linear velocity, which is also determined by the curvature and torsion of the curve at a particular point. For flat curves, there is no sliding, that is, the movable axoid is rolling over a stationary one without sliding. There is a set of curves for which the angular velocity of the rotation of the trihedral is constant. These include the helical line too. The article deals with axoids of cylindrical lines and some of them are constructed.

Injuries to the Coronoid Process of the Ulna with Involvement of the Lesser Sigmoid Notch

2020 ◽  
Author(s):  
Valentin Rausch ◽  
Sina Neugebauer ◽  
Tim Leschinger ◽  
Lars Müller ◽  
Kilian Wegmann ◽  
...  
Keyword(s):  
Fragment Size ◽  
Coronoid Process ◽  
Annular Ligament ◽  
Concomitant Injuries ◽  
Proximal Ulna ◽  
Sigmoid Notch ◽  
Coronoid Fractures ◽  
The Mean ◽  
The Stability ◽  
Arthritic Changes

Abstract Introduction This study aimed to describe the involvement of the lesser sigmoid notch in fractures to the coronoid process. We hypothesized that injuries to the lateral aspect of the coronoid process regularly involve the annular ligament insertion at the anterior lesser sigmoid notch. Material and Methods Patients treated for a coronoid process fracture at our institution between 06/2011 and 07/2018 were included. We excluded patients < 18 years, patients with arthritic changes or previous operative treatment to the elbow, and patients with concomitant injuries to the proximal ulna. In patients with involvement of the lesser sigmoid notch, the coronoid height and fragment size (anteroposterior, mediolateral, and craniocaudal) were measured. Results Seventy-two patients (mean age: 47 years ± 17.6) could be included in the study. Twenty-one patients (29.2%) had a fracture involving the lateral sigmoid notch. The mean anteroposterior fragment length was 7 ± 1.6 mm. The fragment affected a mean of 43 ± 10.8% of the coronoid height. The mean mediolateral size of the fragment was 10 ± 5.0 mm, and the mean cranio-caudal size was 7 ± 2.7 mm. Conclusion Coronoid fractures regularly include the lesser sigmoid notch. These injuries possibly affect the anterior annular ligament insertion which is important for the stability of the proximal radioulnar joint and varus stability of the elbow.

Instant 99mTc-Labelled Glucoheptonate Kit for Kidney Imaging

1983 ◽  
Vol 22 (05) ◽  
pp. 246-250 ◽  
Author(s):  
M. Al-Hilli ◽  
H. M. A. Karim ◽  
M. H. S. Al-Hissoni ◽  
M. N. Jassim ◽  
N. H. Agha
Keyword(s):  
Sodium Hydroxide Solution ◽  
Normal Subjects ◽  
Organ Distribution ◽  
Stable Complex ◽  
Scintillation Camera ◽  
Ph Adjustment ◽  
The Mean ◽  
The Stability ◽  
Kidney Imaging ◽  
Mean Concentration

Gelchromatography column scanning has been used to study the fractions of reduced hydrolyzed 99mTc, 99mTc-pertechnetate and 99mTc-chelate in a 99mTc-glucoheptonate (GH) preparation. A stable high labelling yield of 99mTc-GH complex in the radiopharmaceutical has been obtained with a concentration of 40-50 mg of glucoheptonic acid-calcium salt and not less than 0.45 mg of SnCl2 2 H2O at an optimal pH between 6.5 and 7.0. The stability of the complex has been found significantly affected when sodium hydroxide solution was used for the pH adjustment. However, an alternative procedure for final pH adjustment of the preparation has been investigated providing a stable complex for the usual period of time prior to the injection. The organ distribution and the blood clearance data of 99mTc-GH in rabbits were relatively similar to those reported earlier. The mean concentration of the radiopharmaceutical in both kidneys has been studied in normal subjects for one hour with a scintillation camera and the results were satisfactory.

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