scholarly journals DETECTION OF SPACECRAFT ORBITS IN MULTI-ELEMENT LAUNCHES WITH LOW SCATTERING SPEED. DISTRIBUTION OF MEASUREMENTS OF ORBITS

2019 ◽  
pp. 46-54
Author(s):  
K. V. Sorokin ◽  
L. N. Pylaev
Keyword(s):  
Relative Motion ◽  
Velocity Vector ◽  
Dimensional Space ◽  
Detection Time ◽  
One Dimensional ◽  
Speed Distribution ◽  
Space Objects ◽  
Dense Cluster ◽  
Spacecraft Orbits ◽  
Algorithm Verification

The paper considers the structure of the algorithm for detecting the orbits of spacecraft in multi‑element launches with low speed of scattering. These launches are used in recent years for the launching of microsatellites into orbits. In the proposed algorithm, the difficult task of distributing measurements to orbits is solved on the basis of taking into account the features of the relative motion of nearby space objects that form a dense cluster at launch. In particular, it is proposed to use the relative distance between the spacecraft in the direction of the velocity vector as a distribution parameter. Then the problem of detecting orbits is reduced to the distribution of measurements in one‑dimensional space of relative distances. The developed structure of the algorithm can significantly reduce the detection time and the number of calculations compared to the standard algorithm. Verification of the proposed method on the example of analyzing data on the actual launch of the spacecraft confirmed its effectiveness.

Parametric surfaces

1949 ◽  
Vol 45 (1) ◽  
pp. 14-23 ◽  
Author(s):  
A. S. Besicovitch
Keyword(s):  
Dimensional Space ◽  
Parametric Surfaces ◽  
Rectifiable Curve ◽  
One Dimensional ◽  
Dimensional Measure

In 1914 Carathéodory defined m–dimensional measure in n–dimensional space. He considered one-dimensional measure as a generalization of length and he proved that the length of a rectifiable curve coincides with its one-dimensional measure.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

scholarly journals Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials

2020 ◽  
Vol 10 (24) ◽  
pp. 9123
Author(s):  
Yan Zeng ◽  
Hong Zheng ◽  
Chunguang Li
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Volume Method ◽  
Difference Method ◽  
Legendre Polynomials ◽  
Dimensional Space ◽  
Numerical Manifold Method ◽  
One Dimensional ◽  
Numerical Manifold ◽  
Volume Method

Traditional methods such as the finite difference method, the finite element method, and the finite volume method are all based on continuous interpolation. In general, if discontinuity occurred, the calculation result would show low accuracy and poor stability. In this paper, the numerical manifold method is used to capture numerical discontinuities, in a one-dimensional space. It is verified that the high-degree Legendre polynomials can be selected as the local approximation without leading to linear dependency, a notorious “nail” issue in Numerical Manifold Method. A series of numerical tests are carried out to evaluate the performance of the proposed method, suggesting that the accuracy by the numerical manifold method is higher than that by the later finite difference method and finite volume method using the same number of unknowns.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

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