A high Precision Satellite Positioning Technology without Considering Multi-body Problem and Relativistic Effects

2020 ◽  
Vol 2 (4) ◽  
pp. 169-181
Author(s):  
Zhou Chiyu ◽  
Liu Ting ◽  
Liu Tingting ◽  
Zhou Jie ◽  
Zhang Jiarong ◽  
...  
Keyword(s):  
High Precision ◽  
Body Problem ◽  
Relativistic Effects ◽  
Satellite Positioning ◽  
Multi Body

scholarly journals On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

scholarly journals New relativistic effects in the motion of the Moon

1986 ◽  
Vol 114 ◽  
pp. 407-410
Author(s):  
Bahram Mashhoon
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Relativistic Effects ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
The Moon ◽  
Three Body Problem ◽  
Novel Approach ◽  
Lunar Motion ◽  
Three Body

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.

Study on the Method of Error Identification and Compensation for Gear Measuring Center

2012 ◽  
Vol 482-484 ◽  
pp. 1821-1828
Author(s):  
Peng Wan ◽  
Jun Jie Guo ◽  
Hai Tao Li
Keyword(s):  
High Precision ◽  
Error Detection ◽  
Geometric Error ◽  
Precision Measurements ◽  
Tooth Surface ◽  
Geometric Errors ◽  
Detection Technology ◽  
Accuracy Of Measurement ◽  
Measuring Machine ◽  
Multi Body

Gear Measuring Center(GMC) is commonly used to test error of the tooth surface of the gear, whose geometric accuracy directly impacts on the accuracy of measurement. How to quickly and accurately detect space geometric error of the measuring machine and compensate becomes the essential means of high-precision measurements. According to the problem above, in the paper, three-beams laser detection technology is proposed. The detection of the geometric errors of the linear axis was achieved. The accurate measurement for the position and attitude of the plane mirror on measurement seat was achieved based on laser telemetry principle. The positioning error, the pitching angle errors, the deflection angle errors and the straightness errors were separated. And then based on multi-body system theory, by using of homogeneous coordinate transformation, the error compensation model of 4-axis measuring machine which includes three shifting pairs and one revolute pair was established, and the algorithm was given in the paper. The theoretical foundation for real-time compensation of 4-axis GMC was established. The geometric errors of GMC can be improved by the method of the error detection and compensation. The method plays a very important role in high-precision measurements.

High-precision satellite positioning system as a new tool to study the biomechanics of human locomotion

2000 ◽  
Vol 33 (12) ◽  
pp. 1717-1722 ◽  
Author(s):  
Philippe Terrier ◽  
Quentin Ladetto ◽  
Bertrand Merminod ◽  
Yves Schutz
Keyword(s):  
High Precision ◽  
Human Locomotion ◽  
Positioning System ◽  
Satellite Positioning

scholarly journals Exact Solution for Relativistic Trajectories Using Modal Transseries

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1505
Author(s):  
Luis Acedo ◽  
Abraham J. Arenas ◽  
Nicolas De La Espriella
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
High Precision ◽  
Limit Cycles ◽  
Fundamental Problem ◽  
Orbital Plane ◽  
Relativistic Effects ◽  
Geodesic Equation ◽  
Novel Method ◽  
Analytical Expressions

In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form e−nθ, n=1, 2, …, where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions.

Trajectory evolution in the multi-body problem with applications in the Saturnian system

2011 ◽  
Vol 69 (11-12) ◽  
pp. 1038-1049 ◽  
Author(s):  
Diane Craig Davis ◽  
Kathleen C. Howell
Keyword(s):  
Body Problem ◽  
Saturnian System ◽  
Multi Body
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