Special perturbation theory methods in celestial mechanics. II. Comparative analysis of numerical efficiency

2007 ◽  
Vol 50 (1) ◽  
pp. 78-86
Author(s):  
V. A. Avdyushev
Keyword(s):  
Perturbation Theory ◽  
Comparative Analysis ◽  
Celestial Mechanics ◽  
Numerical Efficiency ◽  
Special Perturbation

scholarly journals Application of Computational Intelligence in Order to Develop Hybrid Orbit Propagation Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Iván Pérez ◽  
Juan Félix San-Juan ◽  
Montserrat San-Martín ◽  
Luis María López-Ochoa
Keyword(s):  
Time Series ◽  
Perturbation Theory ◽  
Computational Intelligence ◽  
General Perturbation ◽  
Special Perturbation ◽  
Statistical Time ◽  
Propagation Methods ◽  
External Forces ◽  
Semianalytical Method ◽  
Earth’S Oblateness

We present a new approach in astrodynamics and celestial mechanics fields, calledhybrid perturbation theory. A hybrid perturbation theory combines anintegrating technique, general perturbation theory or special perturbation theory or semianalytical method, with aforecasting technique, statistical time series model or computational intelligence method. This combination permits an increase in the accuracy of the integrating technique, through the modeling of higher-order terms and other external forces not considered in the integrating technique. In this paper, neural networks have been used as time series forecasters in order to help two economic general perturbation theories describe the motion of an orbiter only perturbed by the Earth’s oblateness.

Celestial mechanics via quaternions

1994 ◽  
Vol 72 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Jan Vrbik
Keyword(s):  
Perturbation Theory ◽  
Celestial Mechanics ◽  
New Technique

The two-body perturbed problem is solved using a modified Kustaanheimo–Stiefel equation recast in a form suitable for perturbation-theory treatment. The power and elegance of the new technique is demonstrated by deriving major components of the Moon's motion in literally a few lines.

PERTURBATIVE EXPANSIONS IN THE INCLUSIVE DECAY OF THE TAU-LEPTON

2002 ◽  
Vol 17 (26) ◽  
pp. 3789-3808 ◽  
Author(s):  
KIMBALL A. MILTON ◽  
OLGA P. SOLOVTSOVA
Keyword(s):  
Perturbation Theory ◽  
Comparative Analysis ◽  
Tau Lepton ◽  
Analytic Approach ◽  
Basic Principles ◽  
Lepton Decay ◽  
Inclusive Decay ◽  
Self Consistency ◽  
Standard Perturbation Theory

A comparative analysis is performed for various forms of perturbative expansions in spacelike and timelike regions. As applied to the inclusive decay of the τ-lepton, comparison is given for the results derived within the framework of the standard perturbation theory and the analytic approach that modernizes perturbative expansions so that the new approximations reflect basic principles of the theory: renormalization invariance, spectrality, and causality. Advantages and self-consistency of the analytic approach in describing τ-lepton decay are demonstrated.

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