scholarly journals Existence of Symmetric Periodic Orbits in the Restricted Problem of Three Bodies in Three-Dimensional Coordinate System.

1963 ◽  
Vol 68 ◽  
pp. 534
Author(s):  
Ram Kishore Choudhary
Keyword(s):  
Coordinate System ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
Symmetric Periodic Orbits ◽  
Three Dimensional Coordinate

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.

scholarly journals The Mechanism of Branching of Three-Dimensional Periodic Orbits from the Plane

1983 ◽  
Vol 74 ◽  
pp. 213-224
Author(s):  
I.A. Robin ◽  
V.V. Markellos
Keyword(s):  
Recent Work ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
General Situation ◽  
Orbital Symmetry ◽  
Resonant Orbits ◽  
Symmetry Properties ◽  
Elliptic Restricted Problem ◽  
Symmetric Periodic Orbits

AbstractA linearised treatment is presented of vertical bifurcations of symmetric periodic orbits(bifurcations of plane with three-dimensional orbits) in the circular restricted problem. Recent work on bifurcations from vertical-critical orbits (av = ±1) is extended to deal with the v more general situation of bifurcations from vertical self-resonant orbits (av = cos(2Πn/m) for integer m,n) and it is shown that in this more general case bifurcating families of three-dimensional orbits always occur in pairs, the orbital symmetry properties being governed by the evenness or oddness of the integer m. The applicability of the theory to the elliptic restricted problem is discussed.

scholarly journals Applications of KS - variables in celestial mechanics

BIBECHANA ◽  
1970 ◽  
Vol 7 ◽  
pp. 54-60
Author(s):  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Coordinate System ◽  
Celestial Mechanics ◽  
Restricted Problem ◽  
Three Dimensional ◽  
Orbital Elements ◽  
Circular Restricted Problem ◽  
Ks Variables ◽  
Three Dimensional Coordinate

This paper deals with the transformation of KS-Variables and canonically conjugate variables from sideral (inertial) to synodic (rotating) form and their applications in "the circular restricted problem of three bodies in three-dimensional coordinate system" to form generating solutions. Keywords: KS - transformation; KS - Variables; Orbital elements; Generating solutions DOI: 10.3126/bibechana.v7i0.4046BIBECHANA 7 (2011) 54-60

Bifurcations of Double Homoclinic Loops in Reversible Systems

2020 ◽  
Vol 30 (16) ◽  
pp. 2050246
Author(s):  
Yuzhen Bai ◽  
Xingbo Liu
Keyword(s):  
Coordinate System ◽  
Periodic Orbits ◽  
Homoclinic Orbit ◽  
Poincaré Map ◽  
Local Coordinate System ◽  
Reversible Systems ◽  
Bifurcation Equation ◽  
Bifurcation Phenomena ◽  
New Type ◽  
Symmetric Periodic Orbits

This paper is devoted to the study of bifurcation phenomena of double homoclinic loops in reversible systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equation, we perform a detailed study to obtain fruitful results, and demonstrate the existence of the R-symmetric large homoclinic orbit of new type near the primary double homoclinic loops, the existence of infinitely many R-symmetric periodic orbits accumulating onto the R-symmetric large homoclinic orbit, and the coexistence of R-symmetric large homoclinic orbit and the double homoclinic loops. The homoclinic bellow can also be found under suitable perturbation. The relevant bifurcation surfaces and the existence regions are located.

Influencing of Coordinate Transformation on Based CGCS2000 on Topographic Map with Large Scales

2014 ◽  
Vol 522-524 ◽  
pp. 1207-1210
Author(s):  
Qing Wu Meng ◽  
Lu Meng
Keyword(s):  
Coordinate System ◽  
Coordinate Transformation ◽  
Grid Point ◽  
Three Dimensional ◽  
Transformation Model ◽  
Topographic Maps ◽  
Topographic Map ◽  
Transformation Parameters ◽  
Coordinate Changes ◽  
Three Dimensional Coordinate

Using three dimensional coordinate transformation model with 7 parameters the coordinate transformation parameters are solved. Comparing the coordinates of the kilometer grid point on topographic maps in Beijing54, Xian80 and Urban Independent Coordinate System with the observation coordinates of same point inCGCS2000, Through watching their coordinate changes the moving changes regularity on topographic maps are discovered between Beijing54 and CGCS2000, between Xian 80 and CGCS2000, Urban Independent Coordinate System and CGCS2000

Chinese Geodetic Coordinate System 2000 and its Comparison with WGS84

2014 ◽  
Vol 580-583 ◽  
pp. 2793-2796 ◽  
Author(s):  
Hou Pu Li ◽  
Shao Feng Bian ◽  
Zhong Mei Li
Keyword(s):  
Coordinate System ◽  
Normal Gravity ◽  
Three Dimensional ◽  
Vertical Gradient ◽  
Coordinate Systems ◽  
Present Measurement ◽  
Three Dimensional Coordinate ◽  
Geodetic Coordinate System ◽  
International Measurement ◽  
Geocentric Coordinate System

It is a general trend to adopt the geocentric coordinate system as a geodetic datum for the international measurement community. The definition and realization of Chinese geocentric three-dimensional coordinate system (CGCS2000) which has been employed since July 1st, 2008 were introduced in detail. The defining parameters and derived constants of the reference ellipsoid used were given. The comparison between CGCS2000 and WGS84 was carried out. The differences of geodetic coordinates of a point between the two coordinate systems, normal gravity and vertical gradient of normal gravity on the two ellipsoids caused by the change of the flattening of the ellipsoid were analyzed. The results show that these differences could be neglected in view of present measurement accuracies.

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