scholarly journals Approximate State Transition Matrix and Secular Orbit Model

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. P. Ramachandran
Keyword(s):  
Orbit Determination ◽  
Transition Matrix ◽  
Numerical Experiments ◽  
State Transition ◽  
Orbital Motion ◽  
The State ◽  
State Transition Matrix ◽  
Reference Orbit ◽  
Determination System ◽  
Orbit Model

The state transition matrix (STM) is a part of the onboard orbit determination system. It is used to control the satellite’s orbital motion to a predefined reference orbit. Firstly in this paper a simple orbit model that captures the secular behavior of the orbital motion in the presence of all perturbation forces is derived. Next, an approximate STM to match the secular effects in the orbit due to oblate earth effect and later in the presence of all perturbation forces is derived. Numerical experiments are provided for illustration.

Numerical Algebra Solution: A New Algorithm for the State Transition Matrix

2017 ◽  
Vol 60 (12) ◽  
pp. 2620-2629 ◽  
Author(s):  
Wenfeng Nie ◽  
Tianhe Xu ◽  
Yujun Du ◽  
Fan Gao ◽  
Guochang Xu
Keyword(s):  
Transition Matrix ◽  
State Transition ◽  
The State ◽  
State Transition Matrix ◽  
Numerical Algebra

The numerical algorithms for discrete Mittag-Leffler functions approximation

2019 ◽  
Vol 22 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Ang Li ◽  
Yiheng Wei ◽  
Zongyang Li ◽  
Yong Wang
Keyword(s):  
Transition Matrix ◽  
State Transition ◽  
Numerical Algorithms ◽  
The State ◽  
State Transition Matrix ◽  
Numerical Implementation ◽  
Science And Engineering ◽  
Implementation Method ◽  
Theoretical Results

Abstract Motivated essentially by the success of the applications of the discrete Mittag-Leffler functions (DMLF) in many areas of science and engineering, the authors present, in a unified manner, a detailed numerical implementation method of the Mittag-Leffler function. With the proposed method, the overflow problem can be well solved. To further improve the practicability, the state transition matrix described by discrete Mittag-Leffler functions are investigated. Some illustrative examples are provided to verify the effectiveness of the proposed theoretical results.

Discussion on Solving Systematic Matrix for Linear System of Invariant Time

2012 ◽  
Vol 249-250 ◽  
pp. 652-656
Author(s):  
Cheng Hao He ◽  
Zhi Hong Yin
Keyword(s):  
Linear System ◽  
Matrix Function ◽  
Transition Matrix ◽  
State Transition ◽  
Computing Methods ◽  
The State ◽  
State Transition Matrix

For a given matrix function, determining whether it meets the conditions of the state transition matrix by utilizing the criteria of the state transition matrix. If satisfied, three computing methods of systematic matrix is deduced through both qualities and relationship with the systematic matrix of the state transition matrix, comparing the characteristics of every method and inspecting availability of each solving method. Finally, the simple way for solving systematic matrix is obtained, which provides reference for solving systematic matrix in practice.

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