Impact of Stochastic Atmospheric Density on Satellite Orbit Stability
Abstract
:1. Introduction
2. Short Review of the Mechanical Aspects of the Satellite
- Reference system Ox1y1z1 is obtained by rotating Oξηζ around axis Oζ with the angular displacement θ.
- Reference system Ox2y2z2 is obtained by further rotating Ox1y1z1 around Oy1 with the angular displacement ψ.
- Principal reference system Oxyz is obtained by rotating Ox2 around with the angular displacement φ; the final axis Ox is the symmetry axis of the satellite.
3. Stochastic Numerical Methods
- -
- Strong convergence:
- -
- Weak convergence:
4. Numerical Simulations
4.1. Test 1. The SDE of a Forced Undamped Oscillator with Exterior Stochastic Disturbance
- A.
- Non-resonant case .
- B.
- Resonant case .
4.2. The Dimensionless SDE of the Pitch Angle of the Satellite
4.2.1. Case 1
4.2.2. Case 2
4.2.3. Case 3
4.2.4. Case 4
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Name of the Scheme | Additive Noise | Multiplicative Noise | ||
---|---|---|---|---|
Weak Order | Strong Order | Weak Order | Strong Order | |
Euler–Maruyama | 1 | 1 | 1 | 0.5 |
Milshtein | 1 | 1 | 1 | 1 |
Stochastic Heun | 2 | 2 | 1 | 1 |
FRKI | 1 | 1 | 1 | 1 |
ERK | 1 | 1 | 1.5 | 1.5 |
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Bogoi, A.; Strătilă, S.; Cican, G.; Crunțeanu, D.-E.; Levențiu, C. Impact of Stochastic Atmospheric Density on Satellite Orbit Stability. Symmetry 2025, 17, 402. https://doi.org/10.3390/sym17030402
Bogoi A, Strătilă S, Cican G, Crunțeanu D-E, Levențiu C. Impact of Stochastic Atmospheric Density on Satellite Orbit Stability. Symmetry. 2025; 17(3):402. https://doi.org/10.3390/sym17030402
Chicago/Turabian StyleBogoi, Alina, Sergiu Strătilă, Grigore Cican, Daniel-Eugeniu Crunțeanu, and Constatin Levențiu. 2025. "Impact of Stochastic Atmospheric Density on Satellite Orbit Stability" Symmetry 17, no. 3: 402. https://doi.org/10.3390/sym17030402
APA StyleBogoi, A., Strătilă, S., Cican, G., Crunțeanu, D.-E., & Levențiu, C. (2025). Impact of Stochastic Atmospheric Density on Satellite Orbit Stability. Symmetry, 17(3), 402. https://doi.org/10.3390/sym17030402