Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits
Abstract
:1. Introduction
- The boundary conditions are being formulated in terms of modified equinoctial elements, with several positive analytical consequences;
- The stability analysis is being extended to target orbits with time-varying orbit elements.
2. Orbit Dynamics
3. Nonlinear Orbit Control
3.1. Formulation of the Problem
3.2. Feedback Control Law
- ;
- (target set).
4. Numerical Simulations
4.1. Target Orbit 1
4.2. Target Orbit 2
5. Discussion of Results
6. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
RAAN | Right Ascension of the Ascending Node |
MCI | Moon Centered Inertial |
LVLH | Local Vertical Local Horizontal |
LH | Local Horizontal |
Appendix A. Planetary Data
Body | |
---|---|
Sun | 132712440018 |
Earth | 398600.4418 |
Moon | 4902.7779 |
Value | Value | ||
---|---|---|---|
0.000203256369305959 | −2.2434487970911 × 10−6 | ||
8.59050334996568 × 10−6 | 4.61610568281654 × 10−6 | ||
−9.8522886746674 × 10−6 | −6.7273906042203 × 10−6 | ||
−1.3293051175382 × 10−5 | 5.54940421259954 × 10−6 | ||
−2.2061158962342 × 10−5 | −4.6246357265911 × 10−6 | ||
−9.4065451772204 × 10−6 | −1.4141219096004 × 10−6 | ||
1.51243401890736 × 10−5 | −1.6209625508441 × 10−6 | ||
3.89230799976237 × 10−6 | 1.29851648071154 × 10−6 | ||
5.14949783632897 × 10−6 | −1.7804783918105 × 10−6 | ||
9.1117958405472 × 10−6 | −1.4541586632206 × 10−6 | ||
−1.4596672751979 × 10−6 | 2.1351214383094 × 10−6 | ||
5.70913026297742 × 10−6 | −1.9588420020059 × 10−6 | ||
−4.7874115985482 × 10−6 | −1.3163362865652 × 10−6 | ||
2.97052872898108 × 10−6 | 1.26894455814441 × 10−6 | ||
1.75163995006724 × 10−6 | −1.0675927011228 × 10−6 | ||
2.34692497584258 × 10−6 | 1.92342072984345 × 10−6 | ||
1.21874850482553 × 10−6 | 1.0580049555114 × 10−6 |
Value | Value | ||
---|---|---|---|
0.000203256369305959 | 0.000415878398442979 | ||
8.59050334996568 × 10−6 | 0.20642811107848 | ||
−9.8522886746674 × 10−6 | 0.16771320834929 | ||
−1.3293051175382 × 10−5 | −0.0496398759987853 | ||
−2.2061158962342 × 10−5 | 2.86012534158749 | ||
−9.4065451772204 × 10−6 | −1.18630809022817 | ||
1.51243401890736 × 10−5 | −1.83532311833521 | ||
3.89230799976237 × 10−6 | −1.01434986302375 | ||
5.14949783632897 × 10−6 | −0.0229903684710072 | ||
9.1117958405472 × 10−6 | 0.11842818400149 | ||
−1.4596672751979 × 10−6 | 1.89596195628963 |
Appendix B. Sensitivity Analysis with Respect to the Gravitational Model
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.04 | 5.18 × 10−1 |
3.09 × 10−4 | 6.70 × 10−5 | |
[deg] | 60.00 | 5.96 × 10−3 |
[deg] | 1.56 × | 2.71 × 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.02 | 4.08 × 10−1 |
3.25 × 10−4 | 6.71 × 10−5 | |
[deg] | 60.00 | 5.75 × 10−3 |
[deg] | 3.62 × | 2.84 × 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.01 | 3.82 × 10−1 |
3.47 × 10−4 | 9.23 × 10−5 | |
[deg] | 60.00 | 6.52 × 10−3 |
[deg] | 1.01 × | 3.32 × 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.01 | 3.82 × 10−1 |
3.47 × 10−4 | 9.13 × 10−5 | |
[deg] | 60.00 | 6.75 × 10−3 |
[deg] | 7.21 × | 3.40 × 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.04 | 4.95 × 10−1 |
3.06 × 10−4 | 6.54 × 10−5 | |
[deg] | 60.00 | 5.65 × 10−3 |
[deg] | 1.62 × | 2.85 × 10−3 |
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Orbital Element | [deg] | [deg] |
---|---|---|
Target orbit 1 | 60 | 300 |
Target orbit 2 | 90 | 300 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1837.96 | 4.83 · 10−2 |
3.20 · 10−4 | 4.15 · 10−6 | |
[deg] | 59.99 | 3.38 · 10−5 |
[deg] | 4.87 · | 9.15 · 10−5 |
Final Mass Ratio | 0.625 | 5.29 · 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.83 | 3.38 · 10−2 |
1.54 · 10−3 | 4.34 · 10−6 | |
[deg] | 59.99 | 8.47 · 10−6 |
[deg] | 8.63 · | 8.63 · 10−4 |
Final Mass Ratio | 0.890 | 2.94 · 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1838.33 | 3.37 · 10−3 |
3.11 · 10−4 | 1.80 · 10−6 | |
[deg] | 90.00 | 2.45 · 10−7 |
[deg] | 1.81 · | 3.68 · 10−7 |
Final Mass Ratio | 0.661 | 1.50 · 10−3 |
Parameter | Mean Value | Standard Deviation |
---|---|---|
[km] | 1837.34 | 1.61 · 10−1 |
2.31 · 10−3 | 6.41 · 10−5 | |
[deg] | 90.00 | 7.43 · 10−7 |
[deg] | 4.42 · | 2.12 · 10−6 |
Final Mass Ratio | 0.911 | 3.56 · 10−3 |
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Leonardi, E.M.; Pontani, M.; Carletta, S.; Teofilatto, P. Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits. Appl. Sci. 2024, 14, 1924. https://doi.org/10.3390/app14051924
Leonardi EM, Pontani M, Carletta S, Teofilatto P. Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits. Applied Sciences. 2024; 14(5):1924. https://doi.org/10.3390/app14051924
Chicago/Turabian StyleLeonardi, Edoardo Maria, Mauro Pontani, Stefano Carletta, and Paolo Teofilatto. 2024. "Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits" Applied Sciences 14, no. 5: 1924. https://doi.org/10.3390/app14051924
APA StyleLeonardi, E. M., Pontani, M., Carletta, S., & Teofilatto, P. (2024). Low-Thrust Nonlinear Orbit Control for Very Low Lunar Orbits. Applied Sciences, 14(5), 1924. https://doi.org/10.3390/app14051924