scholarly journals The zonal satellite problem - I: Near-collision flow

1998 ◽  
pp. 31-36 ◽  
Author(s):  
V. Mioc ◽  
M. Stavinschi
Keyword(s):  
Angular Momentum ◽  
Blow Up ◽  
Rotational Symmetry ◽  
Local Flow ◽  
Physical Motion ◽  
Two Body Problem ◽  
Collision Singularity ◽  
Satellite Problem ◽  
Collision Manifold ◽  
Momentum Integral

The force field described by a potential function of the form U = ?n k=1 ak/rk (r = distance between particles, ak = real parameters) models various concrete situations belonging to astronomy, physics, mechanics, astrodynamics, etc. The two-body problem is being tackled in such a field. The motion equations and the first integrals of energy and angular momentum are established. The McGehee-type coordinates are used to blow up the collision singularity and to paste the resulting manifold on the phase space. The flow on the collision manifold is depicted. Then, using the rotational symmetry of the problem and the angular momentum integral, the local flow near collision is described and interpreted in terms of physical motion.

scholarly journals The zonal satellite problem - II: Near-escape flow

1998 ◽  
pp. 37-41
Author(s):  
V. Mioc ◽  
M. Stavinschi
Keyword(s):  
Angular Momentum ◽  
Phase Space ◽  
Rotational Symmetry ◽  
Equations Of Motion ◽  
First Integrals ◽  
Local Flow ◽  
Satellite Problem ◽  
Set Up ◽  
Momentum Integral

The study of the zonal satellite problem is continued by tackling the situation r??. New equations of motion (for which the infinite distance is a singularity) and the corresponding first integrals of energy and angular momentum are set up. The infinity singularity is blown up via McGehee-type transformations, and the infinity manifold is pasted on the phase space. The fictitious flow on this manifold is described. Then, resorting to the rotational symmetry of the problem and to the angular momentum integral, the near-escape local flow is depicted. The corresponding phase curves are interpreted as physical motions.

scholarly journals Collision dynamics in Hénon-Heiles’ two-body problem

2003 ◽  
pp. 43-46 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Body Problem ◽  
Blow Up ◽  
Collision Dynamics ◽  
Two Body Problem ◽  
Collision Singularity ◽  
Collision Manifold ◽  
Special Case

We tackle the two-body problem associated to H?non-Heiles? potential in the special case of the collision singularity. Using McGehee-type transformations of the second kind, we blow up the singularity and replace it by the collision manifold Mc pasted on the phase spece. We fully describe the flow on Mc. This flow is similar to analogous flows met in post-Newtonian two-body problems.

scholarly journals The zonal satellite problem. III Symmetries

2002 ◽  
pp. 1-8
Author(s):  
V. Mioc
Keyword(s):  
Force Field ◽  
Body Problem ◽  
Blow Up ◽  
Polar Coordinates ◽  
Two Body Problem ◽  
Satellite Problem ◽  
Group Of Symmetries

The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n) ak/rk (r = distance between particles, ak = real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita?s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.

scholarly journals Symmetries in central-force problems

2003 ◽  
pp. 47-52 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Vector Fields ◽  
Body Problem ◽  
Blow Up ◽  
Central Force ◽  
Polar Coordinates ◽  
Global Flow ◽  
Two Body Problem ◽  
Concrete Problem ◽  
Central Force Problems ◽  
Force Problem

The two-body problem in central fields (reducible to a central-force problem) models a lot of concrete astronomical situations. The corresponding vector fields (in Cartesian and polar coordinates, extended via collision-blow-up and infinity-blow-up transformations) exhibit nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. All these groups are isomorphic, which is not a trivial result, given the different structures of the corresponding phase spaces. Each of these groups contains seven four-element subgroups isomorphic to Klein?s group. These symmetries are of much help in understanding various characteristics of the global flow of the general problem or of a concrete problem at hand, and are essential in searching for periodic orbits.

scholarly journals Two-body problem in presence of cosmological constant

2019 ◽  
Vol 28 (12) ◽  
pp. 1950155
Author(s):  
G. S. Bisnovatyi-Kogan ◽  
M. Merafina
Keyword(s):  
Angular Momentum ◽  
Cosmological Constant ◽  
Body Problem ◽  
Local Group ◽  
Classical Case ◽  
Virgo Cluster ◽  
Body Motion ◽  
Critical Parameters ◽  
Two Body Problem ◽  
Qualitative Picture

We consider the Kepler two-body problem in presence of the cosmological constant [Formula: see text]. Contrary to the classical case, where finite solutions exist for any angular momentum of the system [Formula: see text], in presence of [Formula: see text] finite solutions exist only in the interval [Formula: see text]. The qualitative picture of the two-body motion is described, and critical parameters of the problem are found. Application is made to the relative motion of the Local Group and Virgo cluster.

DESCRIPTION OF THE PAIRING CORRELATION FOR A STRONG COUPLING REGIME WITHOUT BREAKING THE ROTATIONAL SYMMETRY

1992 ◽  
Vol 07 (04) ◽  
pp. 725-736 ◽  
Author(s):  
N. SANDULESCU ◽  
A. A. RADUTA
Keyword(s):  
Angular Momentum ◽  
Single Particle ◽  
Rotational Symmetry ◽  
Strong Coupling Regime ◽  
Pairing Correlation ◽  
System A ◽  
Gap Parameter ◽  
Orthogonal Set ◽  
Specific Influence ◽  
Single Particle Basis

By projecting out the lowest angular momentum from an orthogonal set of intrinsic functions describing a particle-core interacting system, a single-particle basis is obtained.1 This basis is used for describing a system of nucleons which interact among themselves by pairing forces. The specific influence of both the shell structure and the gap parameter is explicitly given.

scholarly journals On-Chip Guiding of Higher-Order Orbital Angular Momentum Modes

Photonics ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 72 ◽  
Author(s):  
In Joon Lee ◽  
Sangin Kim
Keyword(s):  
Angular Momentum ◽  
Field Distribution ◽  
Orbital Angular Momentum ◽  
Rotational Symmetry ◽  
Higher Order ◽  
Waveguide Structure ◽  
Rotation Symmetry ◽  
Gaussian Mode ◽  
On Chip ◽  
Topological Charges

Higher-order orbital angular momentum (OAM) mode guiding in a waveguide which is suitable for on-chip integration has been investigated. Based on the relation between the Laguerre-Gaussian mode and the Hermite-Gaussian mode, it has been shown that two degenerate guided modes of π/2l-rotation symmetry can support the l-th order OAM mode. In order to mimic the rotational symmetry, we have proposed the waveguide structure of a cross-shaped core and designed a waveguide that can support OAM modes of ±1 and ±2 topological charges simultaneously at a wavelength of 1550 nm. Purity of the OAM modes guided in the designed waveguide has been assessed by numerically calculating their topological charges from the field distribution, which were close to the theoretical values. We also investigated the guiding of OAM modes of ±3 and ±4 topological charges in our proposed waveguide structure, which revealed the possibility of the separate guiding of those OAM modes with relatively lower purity.

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