Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem
Abstract
:1. Introduction
2. Description of the Problem
3. Mathematical Formulation of the Problem
3.1. Nonlinear Equations for Terminal Constraints
3.2. Nonlinear Equations for Coplanar Lambert Problem
4. Numerical Method without Derivation for the Two Equations
4.1. Solution of Lambert Problem without Derivation
4.2. Solution of Single-Impulse Flyby Two Co-Orbital Spacecraft Problem without Derivation
5. Numerical Examples
5.1. The Lambert Problem
5.2. The Single-Impulse Flyby Co-Orbital Spacecraft Problem
Random Initial Orbital Elements
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Glossary
Length of the transfer chord | |
Eccentricity vector of orbit | |
Eccentricity of orbit | |
Perpendicular component of the transfer chord | |
Parallel component of the transfer chord | |
Mean anomaly of spacecraft at time | |
Mean motion of orbit | |
Semi-latus rectum of orbit | |
Position of spacecraft at time | |
Distance between spacecraft and earth center at time | |
Anomaly of spacecraft at time | |
Perigee of orbit | |
Angle between perigees of two orbits (from to ) |
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Average Computation Time (ms) | 1000 Times | 10,000 Times | 50,000 Times | 100,000 Times | Efficiency Improvement |
---|---|---|---|---|---|
Universal variable method [35] | 1.3581 | 1.3593 | 1.3547 | 1.3543 | 92.09% |
Traversal search method | 0.2120 | 0.2039 | 0.1977 | 0.1972 | 45.69% |
Our method | 0.1118 | 0.1114 | 0.1075 | 0.1071 |
Spacecraft | (°) | (°) | (°) | (°) | ||
---|---|---|---|---|---|---|
7134 | 7861 | 23 | 11 | 38 | 17 | |
9871 | 10,306 | 40 | 81 | |||
82 |
Spacecraft | (°) | (°) | (°) | (°) | ||
---|---|---|---|---|---|---|
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Su, H.; Dong, Z.; Liu, L.; Xia, L. Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem. Aerospace 2022, 9, 374. https://doi.org/10.3390/aerospace9070374
Su H, Dong Z, Liu L, Xia L. Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem. Aerospace. 2022; 9(7):374. https://doi.org/10.3390/aerospace9070374
Chicago/Turabian StyleSu, Haoxiang, Zhenghong Dong, Lihao Liu, and Lurui Xia. 2022. "Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem" Aerospace 9, no. 7: 374. https://doi.org/10.3390/aerospace9070374