Equations of motion of the restricted problem of (2 + 2) bodies when primaries are magnetic dipoles and minor bodies are taken as electric dipoles

1996 ◽  
Vol 64 (4) ◽  
pp. 305-312 ◽  
Author(s):  
A. Prasad ◽  
Bhola Ishwar
Keyword(s):  
Restricted Problem ◽  
Equations Of Motion ◽  
Magnetic Dipoles ◽  
Electric Dipoles

Equations of motion of elliptic restricted problem of three bodies with variable mass

1988 ◽  
Vol 45 (4) ◽  
pp. 387-393 ◽  
Author(s):  
R. K. Das ◽  
A. K. Shrivastava ◽  
B. Ishwar
Keyword(s):  
Restricted Problem ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Elliptic Restricted Problem

Stable Divergence Angles of a Magnetic Dipole Spiral Array

1997 ◽  
Vol 11 (24) ◽  
pp. 1069-1075
Author(s):  
X. D. Fan ◽  
L. A. Bursill
Keyword(s):  
Nearest Neighbor ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Divergence Angle ◽  
Magnetic Dipoles ◽  
Analytical Proof ◽  
The Difference ◽  
Spiral Array ◽  
Map Analysis ◽  
Neighbor Approximation

An analytical model is introduced for the experiment of Douady and Couder [Phys. Rev. Lett.68, 2098 (1992), where phyllotactic patterns appear as a dynamical result of the interaction between magnetic dipoles. The difference equation for the divergence angle (i.e. the angle between successive radial vectors) is obtained by solving the equations of motion with a second nearest neighbor (SNN) approximation. A one-dimensional map analysis as well as a comprehensive analytical proof shows that the divergence angle always converges to a single attractor regardless of the initial conditions. This attractor is approximately the Fibonacci angle(~ 138°) within variations due to a growth factor μ of the pattern. The system is proved to be stable with the SNN approximation. Further analysis with a third nearest neighbor approximation (TNN) shows extra linearly stable attractors may appear around the Lucas angle (~ 99.5°).

scholarly journals The correct and unusual coordinate transformation rules for electromagnetic quadrupoles

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170652 ◽  
Author(s):  
J. Gratus ◽  
T. Banaszek
Keyword(s):  
Coordinate Transformation ◽  
Equations Of Motion ◽  
Flat Space ◽  
Polar Coordinates ◽  
Cartesian Coordinates ◽  
Transformation Rules ◽  
Integral Transformations ◽  
Second Derivatives ◽  
Electric Dipoles ◽  
Derivatives Of

Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat space–time due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordinate transformation and an integral. Transformations involving integrals have not been seen before. This is significantly different from the familiar transformation rules for a dipole, where the components transform as tensors. It enables quadrupoles to be correctly defined in general relativity and to prescribe the equations of motion for a quadrupole in a coordinate system adapted to its motion and then transform them to the laboratory coordinates. An example is given of another unusual feature: a quadrupole which is free of dipole terms in polar coordinates has dipole terms in Cartesian coordinates. It is shown that dipoles, electric dipoles, quadrupoles and electric quadrupoles can be defined without reference to a metric and in a coordinates-free manner. This is particularly useful given their complicated coordinate transformation.

scholarly journals Electric dipoles vs. magnetic dipoles —For two molecules in a harmonic trap

2017 ◽  
Vol 118 (6) ◽  
pp. 66002 ◽  
Author(s):  
Wojciech Górecki ◽  
Kazimierz Rzążewski
Keyword(s):  
Harmonic Trap ◽  
Magnetic Dipoles ◽  
Electric Dipoles

scholarly journals Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Awadhesh Kumar Poddar ◽  
Divyanshi Sharma
Keyword(s):  
Perturbation Theory ◽  
Rigid Body ◽  
Coordinate System ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
General Perturbation ◽  
Triaxial Rigid Body ◽  
Three Dimensional Coordinate

AbstractIn this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

A study of downhole electromagnetic sources for mapping enhanced oil recovery processes

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 534-545 ◽  
Author(s):  
Gregory A. Newman
Keyword(s):  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Magnetic Dipoles ◽  
Instrumental Noise ◽  
Recovery Processes ◽  
Before And After ◽  
Order Of Magnitude ◽  
Electric Dipoles ◽  
Eor Processes ◽  
Electric Source

An evaluation of downhole electromagnetic (EM) sources has been made for mapping 3-D enhanced oil recovery (EOR) processes. Two types of sources considered were vertical magnetic dipoles and vertical to near‐vertical electric dipoles and bipoles. These sources were used to produce magnetic field responses expected of EOR processes for crosswell configurations. A borehole‐to‐surface configuration was also studied for the downhole electric source, since this configuration can be highly sensitive to shallow 3-D EOR targets. For the crosswell arrays, the criteria used to evaluate the sources were the magnitudes of the observed signals with and without the process and the amount these signals change because of a migrating process. Instrumental noise was considered in the evaluation. Findings show that either electric or magnetic sources can produce truly significant changes in the fields, provided the fields before and after the initiation of the process are compared. An order of magnitude change in the fields has been demonstrated. The key to measuring such changes is to use the highest frequency possible. This frequency will be limited by instrumental noise. A migrating process did not produce field changes that are as large as those observed with and without the process. Nevertheless, model simulations showed that changes in the fields caused by the migrating processes are significant and measurable. Calculated responses of a shallow process at the surface showed that they were extremely sensitive to small deviations in the orientation of the downhole electric source. Quantitative interpretation should proceed only with techniques that explicitly consider the source orientation.

Equations of motion of the restricted problem of three bodies with variable mass

1983 ◽  
Vol 30 (3) ◽  
pp. 323-328 ◽  
Author(s):  
A. K. Shrivastava ◽  
Bhola Ishwar
Keyword(s):  
Restricted Problem ◽  
Equations Of Motion ◽  
Variable Mass
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