Generalization of Hamilton–Ishlinskii Solid Angle Theorem for Spatial Motion of a Solid Body and its Applications

2019 ◽  
Vol 54 (8) ◽  
pp. 1227-1239
Author(s):  
Yu. N. Chelnokov
Keyword(s):  
Solid Body ◽  
Solid Angle ◽  
Spatial Motion

scholarly journals Trajectory control of solid body spatial motion

2017 ◽  
pp. 704-711 ◽  
Author(s):  
Jian Wang ◽  
A.Yu. Krasnov ◽  
Yu.A. Kapitanyuk ◽  
S.A. Chepinsky ◽  
S.A. Kholunin ◽  
...  
Keyword(s):  
Solid Body ◽  
Trajectory Control ◽  
Spatial Motion

scholarly journals Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

2021 ◽  
Vol 24 (4) ◽  
pp. 17-24
Author(s):  
V.M. Churkin ◽  
T.Yu. Churkina ◽  
A.M. Girin
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Body ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Spatial Motion ◽  
Mathematical Task ◽  
Spatial Movement ◽  
Elastic Thread ◽  
The Mathematical Model

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

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.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

Contrast in Scanning Images of Thin Crystals

1972 ◽  
Vol 30 ◽  
pp. 520-521
Author(s):  
S. Kimoto ◽  
H. Hashimoto ◽  
S. Takashima ◽  
R. M. Stern ◽  
T. Ichinokawa
Keyword(s):  
Crystal Surface ◽  
Solid Angle ◽  
Incident Angle ◽  
Intensity Variation ◽  
Lattice Defects ◽  
Scanning Microscope ◽  
Electron Detector ◽  
Backscattered Electrons ◽  
Electron Image ◽  
Backscattered Electron

The most well known application of the scanning microscope to the crystals is known as Coates pattern. The contrast of this image depends on the variation of the incident angle of the beam to the crystal surface. The defect in the crystal surface causes to make contrast in normal scanning image with constant incident angle. The intensity variation of the backscattered electrons in the scanning microscopy was calculated for the defect in the crystals by Clarke and Howie. Clarke also observed the defect using a scanning microscope.This paper reports the observation of lattice defects appears in thin crystals through backscattered, secondary and transmitted electron image. As a backscattered electron detector, a p-n junction detector of 0.9 π solid angle has been prepared for JSM-50A. The gain of the detector itself is 1.2 x 104 at 50 kV and the gain of additional AC amplifier using band width 100 Hz ∼ 10 kHz is 106.

High spatial resolution x-ray microanalysis of interfaces

1995 ◽  
Vol 53 ◽  
pp. 284-285
Author(s):  
J. R. Michael
Keyword(s):  
Spatial Resolution ◽  
Electron Probe ◽  
Solid Angle ◽  
Collection Efficiency ◽  
Spatial Scales ◽  
Energy Dispersive Spectrometer ◽  
X Rays ◽  
X Ray ◽  
Probe Size ◽  
Brightness Field

X-ray microanalysis in the analytical electron microscope (AEM) refers to a technique by which chemical composition can be determined on spatial scales of less than 10 nm. There are many factors that influence the quality of x-ray microanalysis. The minimum probe size with sufficient current for microanalysis that can be generated determines the ultimate spatial resolution of each individual microanalysis. However, it is also necessary to collect efficiently the x-rays generated. Modern high brightness field emission gun equipped AEMs can now generate probes that are less than 1 nm in diameter with high probe currents. Improving the x-ray collection solid angle of the solid state energy dispersive spectrometer (EDS) results in more efficient collection of x-ray generated by the interaction of the electron probe with the specimen, thus reducing the minimum detectability limit. The combination of decreased interaction volume due to smaller electron probe size and the increased collection efficiency due to larger solid angle of x-ray collection should enhance our ability to study interfacial segregation.

Angular Resolved Electron Spectroscopy with Parallel Recording

1990 ◽  
Vol 48 (2) ◽  
pp. 370-371
Author(s):  
Huang Min ◽  
P.S. Flora ◽  
C.J. Harland ◽  
J.A. Venables
Keyword(s):  
Electron Spectroscopy ◽  
Low Voltage ◽  
Solid Angle ◽  
Detection System ◽  
Voltage Electron ◽  
Cylindrical Mirror ◽  
Inner Radius ◽  
Channel Plate ◽  
And Performance ◽  
Type Detector

A cylindrical mirror analyser (CMA) has been built with a parallel recording detection system. It is being used for angular resolved electron spectroscopy (ARES) within a SEM. The CMA has been optimised for imaging applications; the inner cylinder contains a magnetically focused and scanned, 30kV, SEM electron-optical column. The CMA has a large inner radius (50.8mm) and a large collection solid angle (Ω > 1sterad). An energy resolution (ΔE/E) of 1-2% has been achieved. The design and performance of the combination SEM/CMA instrument has been described previously and the CMA and detector system has been used for low voltage electron spectroscopy. Here we discuss the use of the CMA for ARES and present some preliminary results.The CMA has been designed for an axis-to-ring focus and uses an annular type detector. This detector consists of a channel-plate/YAG/mirror assembly which is optically coupled to either a photomultiplier for spectroscopy or a TV camera for parallel detection.

Comparison of high-angle take-off and low-angle take-off EDX detector geometry of the HF-2000 FE-TEM

1993 ◽  
Vol 51 ◽  
pp. 252-253
Author(s):  
Y. Sato ◽  
T. Hashimoto ◽  
M. Ichihashi ◽  
Y. Ueki ◽  
K. Hirose ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Field Emission ◽  
Solid Angle ◽  
Energy Dispersive ◽  
Objective Lens ◽  
X Rays ◽  
High Angle ◽  
X Ray ◽  
Detector Geometry

Analytical TEMs have two variations in x-ray detector geometry, high and low angle take off. The high take off angle is advantageous for accuracy of quantitative analysis, because the x rays are less absorbed when they go through the sample. The low take off angle geometry enables better sensitivity because of larger detector solid angle.Hitachi HF-2000 cold field emission TEM has two versions; high angle take off and low angle take off. The former allows an energy dispersive x-ray detector above the objective lens. The latter allows the detector beside the objective lens. The x-ray take off angle is 68° for the high take off angle with the specimen held at right angles to the beam, and 22° for the low angle take off. The solid angle is 0.037 sr for the high angle take off, and 0.12 sr for the low angle take off, using a 30 mm2 detector.

Three-Dimensional Reconstruction of Native Androctonus Australis Hemocyanin

1990 ◽  
Vol 48 (1) ◽  
pp. 452-453
Author(s):  
Nicolas Boisset ◽  
Jean-Christophe Taveau ◽  
Jean Lamy ◽  
Terence Wagenknecht ◽  
Michael Radermacher ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Solid Body ◽  
Body Surface ◽  
Three Dimensional ◽  
Staining Technique ◽  
Three Dimensional Reconstruction ◽  
Dimensional Reconstruction ◽  
View Reconstruction ◽  
Surface Representations ◽  
Top View

Hemocyanin, the respiratory pigment of the scorpion Androctonus australis is composed of 24 kidney shaped subunits. A model of architecture supported by many indirect arguments has been deduced from electron microscopy (EM) and immuno-EM. To ascertain, the disposition of the subunits within the oligomer, the 24mer was submitted to three-dimensional reconstruction by the method of single-exposure random-conical tilt series.A sample of native hemocyanin, prepared with the double layer negative staining technique, was observed by transmisson electron microscopy under low-dose conditions. Six 3D-reconstructions were carried out indenpendently from top, side and 45°views. The results are composed of solid-body surface representations, and slices extracted from the reconstruction volume.The main two characters of the molecule previously reported by Van Heel and Frank, were constantly found in the solid-body surface representations. These features are the presence of two different faces called flip and flop and a rocking of the molecule around an axis passing through diagonnally opposed hexamers. Furthermore, in the solid-body surface of the top view reconstruction, the positions and orientations of the bridges connecting the half molecules were found in excellent agreement with those predicted by the model.

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

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