International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12
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 Volume 12, Issue 1 (January 2025), Pages: 30-51

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 Review Paper

Coupled differential-algebraic equations framework for modeling six-degree-of-freedom flight dynamics of asymmetric fixed-wing aircraft

 Author(s): 

 Osama A. Marzouk *

 Affiliation(s):

 College of Engineering, University of Buraimi, Al Buraimi, Oman

 Full text

  Full Text - PDF

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-1435-5318

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2025.01.004

 Abstract

This study presents a comprehensive mathematical framework for modeling the flight dynamics of a six-degree-of-freedom fixed-wing aircraft as a rigid body with three control surfaces: rudder, elevators, and ailerons. The framework consists of 35 differential-algebraic equations (DAEs) and requires 30 constants to be specified. It supports both direct and inverse flight dynamics analyses. In direct dynamics, the historical profiles of control inputs (deflection angles and engine thrust) are specified, and the resulting flight trajectory is predicted. In inverse dynamics, the desired flight trajectory and an additional constraint are specified to determine the required control inputs. The framework employs wind axes for linear-momentum equations and body axes for angular-momentum equations, incorporates two flight path angles, and provides formulas for aerodynamic force and moment coefficients. Key advantages include improved computational efficiency, elimination of Euler angle singularities, and independence from symmetry assumptions with regard to the aircraft’s moments of inertia. The model also accounts for nonlinear air density variations with altitude, up to 20 km above mean sea level, making it suitable for accurate and efficient flight dynamics simulations.

 © 2024 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Flight dynamics, Fixed-wing aircraft, Control surfaces, Differential-algebraic equations, Aerodynamic coefficients

 Article history

 Received 28 August 2024, Received in revised form 7 December 2024, Accepted 15 December 2024

 Acknowledgment

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Marzouk OA (2025). Coupled differential-algebraic equations framework for modeling six-degree-of-freedom flight dynamics of asymmetric fixed-wing aircraft. International Journal of Advanced and Applied Sciences, 12(1): 30-51

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 

 Tables

 Table 1 Table 2 Table 3 

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 References (142)

  1. Abbaszadehmosayebi G and Ganippa L (2014). Determination of specific heat ratio and error analysis for engine heat release calculations. Applied Energy, 122: 143–150. https://doi.org/10.1016/j.apenergy.2014.01.028   [Google Scholar]
  2. Abbott IH (2012). Theory of wing sections: Including a summary of airfoil data. Dover Publications, Mineola, USA.   [Google Scholar]
  3. Akasaka R, Huber ML, Simoni LD, and Lemmon EW (2023). A Helmholtz energy equation of state for trans-1,1,1,4,4,4-hexafluoro-2-butene [R-1336mzz(E)] and an auxiliary extended corresponding states model for the transport properties. International Journal of Thermophysics, 44(4): 50. https://doi.org/10.1007/s10765-022-03143-5   [Google Scholar]
  4. Andreu Angulo I and Ansell PJ (2019). Influence of aspect ratio on dynamic stall of a finite wing. AIAA Journal, 57(7): 2722–2733. https://doi.org/10.2514/1.J057792   [Google Scholar]
  5. Ao Y, Wu K, Lu H, Ji F, and Fan X (2023). Combustion dynamics of high Mach number scramjet under different inflow thermal nonequilibrium conditions. Acta Astronautica, 208: 281–295. https://doi.org/10.1016/j.actaastro.2023.04.020   [Google Scholar]
  6. Aslanov VS (2017). Removal of large space debris by a tether tow. In: Aslanov V (2017). Rigid body dynamics for space applications: 255–356. Butterworth-Heinemann, Oxford, UK. https://doi.org/10.1016/B978-0-12-811094-2.00005-4   [Google Scholar]
  7. Atasay N, Atmanli A, and Yilmaz N (2023). Liquid cooling flow field design and thermal analysis of proton exchange membrane fuel cells for space applications. International Journal of Energy Research, 2023: 7533993. https://doi.org/10.1155/2023/7533993   [Google Scholar]
  8. Barman S and Sinha M (2023a). Satellite attitude control using double-gimbal variable-speed control moment gyro with unbalanced rotor. Journal of Guidance, Control, and Dynamics, 46(5): 838–855. https://doi.org/10.2514/1.G006913   [Google Scholar]
  9. Barman S and Sinha M (2023b). Satellite attitude control using double-gimbal variable-speed control moment gyroscope: Single-loop control formulation. Journal of Guidance, Control, and Dynamics, 46(7): 1314–1330. https://doi.org/10.2514/1.G007054   [Google Scholar]
  10. Bar-Meir G (2022). Basics of fluid mechanics. Zenodo, Geneva, Switzerland.   [Google Scholar]
  11. Beknalkar S, Bryant M, and Mazzoleni A (2024). Algorithm for locomotion mode selection, energy estimation and path planning for a multi-terrain screw-propelled vehicle for arctic exploration. In the IEEE International Conference on Advanced Intelligent Mechatronics, IEEE, Boston, USA: 1462-1467. https://doi.org/10.1109/AIM55361.2024.10636948   [Google Scholar]
  12. Blajer W, Graffstein J, and Krawczyk M (2009). Modeling of aircraft prescribed trajectory flight as an inverse simulation problem. In: Awrejcewicz J (Ed.), Modeling, simulation and control of nonlinear engineering dynamical systems: 153–162. Springer, Amsterdam, Netherlands. https://doi.org/10.1007/978-1-4020-8778-3_14   [Google Scholar]
  13. Braca P, Willett P, LePage K, Marano S, and Matta V (2014). Bayesian tracking in underwater wireless sensor networks with port-starboard ambiguity. IEEE Transactions on Signal Processing, 62(7): 1864–1878. https://doi.org/10.1109/TSP.2014.2305640   [Google Scholar]
  14. Bravo-Mosquera PD, Catalano FM, and Zingg DW (2022). Unconventional aircraft for civil aviation: A review of concepts and design methodologies. Progress in Aerospace Sciences, 131: 100813. https://doi.org/10.1016/j.paerosci.2022.100813   [Google Scholar]
  15. Brezov D (2024). Using rotations to control observable relativistic effects. Mathematics, 12(11): 1676. https://doi.org/10.3390/math12111676   [Google Scholar]
  16. Brincklow JR, Montgomery ZS, and Hunsaker DF (2024). Controlling roll-yaw coupling with aileron and twist design. The Aeronautical Journal, 128(1327): 1961–1973. https://doi.org/10.1017/aer.2024.21   [Google Scholar]
  17. Cardona JJ M, Cardona M, Canales-Verdial JI, and Ordoñez-Avila JL (2024). Direct and inverse kinematics of a 3RRR symmetric planar robot: An alternative of active joints. Symmetry, 16(5): 590. https://doi.org/10.3390/sym16050590   [Google Scholar]
  18. Cavell GC, Osenkowsky TG, Layer DH, Pizzi S, and Hayes WT (2018). National association of broadcasters engineering handbook. 11th Edition, Taylor and Francis Group, Oxfordshire, UK.   [Google Scholar]
  19. Chen K, Yan J, and Huang P (2006). Design of air data system of an aircraft integrated electronic standby instrument. In the International Conference on Mechatronics and Automation, IEEE, Luoyang, China: 1147-1151. https://doi.org/10.1109/ICMA.2006.257787   [Google Scholar]
  20. Custodio D, Henoch CW, and Johari H (2015). Aerodynamic characteristics of finite span wings with leading-edge protuberances. AIAA Journal, 53(7): 1878–1893. https://doi.org/10.2514/1.J053568   [Google Scholar]
  21. Das SK and Chatterjee D (2023). Thermodynamics of phase change. In: Das SK and Chatterjee D (Eds.), Vapor liquid two phase flow and phase change: 61–78. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-031-20924-6_3   [Google Scholar]
  22. De Paula PA, Dos Santos MF, Mercorelli P, and Schettino VB (2024). PID controller application in a gimbal construction for camera stabilization and tracking. In the 25th International Carpathian Control Conference, IEEE, Krynica Zdrój, Poland: 1-6. https://doi.org/10.1109/ICCC62069.2024.10569310   [Google Scholar] PMid:39029723
  23. Della Posta G, Fratini M, Salvadore F, and Bernardini M (2024). Direct numerical simulation of boundary layers over microramps: Mach number effects. AIAA Journal, 62(2): 542–556. https://doi.org/10.2514/1.J063363   [Google Scholar]
  24. Deng Y, Ridley AJ, and Wang W (2008). Effect of the altitudinal variation of the gravitational acceleration on the thermosphere simulation. Journal of Geophysical Research: Space Physics, 113: A09302. https://doi.org/10.1029/2008JA013081   [Google Scholar]
  25. Dimitrios D and Maria S (2018). Assessing air transport socio-economic footprint. International Journal of Transportation Science and Technology, 7(4): 283–290. https://doi.org/10.1016/j.ijtst.2018.07.001   [Google Scholar]
  26. Duben AJ (2024). Critical properties and real gases. In: Duben AJ (Ed.), Case studies in the virtual physical chemistry laboratory: 17–50. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-031-55018-8_2   [Google Scholar]
  27. Durham W (2013). Aircraft flight dynamics and control. John Wiley and Sons, Hoboken, USA.   [Google Scholar]
  28. Ferreira AP and Gimeno L (2024). Determining precipitable water vapour from upper-air temperature, pressure and geopotential height. Quarterly Journal of the Royal Meteorological Society, 150(758): 484–522. https://doi.org/10.1002/qj.4609   [Google Scholar]
  29. Fix AJ, Oh J, Braun JE, and Warsinger DM (2024). Dual-module humidity pump for efficient air dehumidification: Demonstration and performance limitations. Applied Energy, 360: 122771. https://doi.org/10.1016/j.apenergy.2024.122771   [Google Scholar]
  30. Fu H, Song E, and Tong R (2023a). A numerical model for hydrothermal transport in unsaturated freezing soils considering thermodynamics equilibrium. International Journal for Numerical and Analytical Methods in Geomechanics, 47(5): 736–758. https://doi.org/10.1002/nag.3490   [Google Scholar]
  31. Fu Q, Lei L, Chen W, Ren Z, He G, and Liu C (2023b). Effect of mainstream Mach number on the flow characteristics and cooling effectiveness of supersonic film cooling. Numerical Heat Transfer, Part A: Applications. https://doi.org/10.1080/10407782.2023.2287535   [Google Scholar]
  32. Gallup MG (2023). Inverse simulation of autogyros. Journal of the American Helicopter Society, 68(4): 42001–42010. https://doi.org/10.4050/JAHS.68.042001   [Google Scholar]
  33. Garrett SL (2020). Ideal gas laws. In Garrett SL (Ed.), Understanding acoustics: An experimentalist's view of sound and vibration: 333–356. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-030-44787-8_7   [Google Scholar]
  34. Geissler W and van der Wall BG (2017). Dynamic stall control on flapping wing airfoils. Aerospace Science and Technology, 62: 1–10. https://doi.org/10.1016/j.ast.2016.12.008   [Google Scholar]
  35. Genç MS, Kaynak Ü, and Lock GD (2009). Flow over an aerofoil without and with a leading-edge slat at a transitional Reynolds number. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 223(3): 217–231. https://doi.org/10.1243/09544100JAERO434   [Google Scholar]
  36. Georgiadis NJ, Wernet MP, Locke RJ, and Eck Dennis G (2024). Mach number and heating effects on turbulent supersonic jets. AIAA Journal, 62(1): 31–51. https://doi.org/10.2514/1.J063186   [Google Scholar]
  37. Gerkema T and Duran-Matute M (2017). Interannual variability of mean sea level and its sensitivity to wind climate in an inter-tidal basin. Earth System Dynamics, 8(4): 1223–1235. https://doi.org/10.5194/esd-8-1223-2017   [Google Scholar]
  38. Geske AM, Herold DM, and Kummer S (2024). Artificial intelligence as a driver of efficiency in air passenger transport: A systematic literature review and future research avenues. Journal of the Air Transport Research Society, 3: 100030. https://doi.org/10.1016/j.jatrs.2024.100030   [Google Scholar]
  39. Gohardani AS, Doulgeris G, and Singh R (2011). Challenges of future aircraft propulsion: A review of distributed propulsion technology and its potential application for the all electric commercial aircraft. Progress in Aerospace Sciences, 47(5): 369–391. https://doi.org/10.1016/j.paerosci.2010.09.001   [Google Scholar]
  40. Guo J, Shang H, Cai G, Jin Y, Wang K, and Li S (2023). Early detection of coal spontaneous combustion by complex acoustic waves in a concealed fire source. ACS Omega, 8(19): 16519–16531. https://doi.org/10.1021/acsomega.3c00199   [Google Scholar] PMid:37214726 PMCid:PMC10193550
  41. Hammer PR, Garmann DJ, and Visbal MR (2022). Effect of aspect ratio on finite-wing dynamic stall. AIAA Journal, 60(12): 6581–6593. https://doi.org/10.2514/1.J062109   [Google Scholar]
  42. Han Q, Jiang Z, and Chu F (2023). Micro-vibration modeling and analysis of single-gimbal control moment gyros. Communications in Nonlinear Science and Numerical Simulation, 118: 107040. https://doi.org/10.1016/j.cnsns.2022.107040   [Google Scholar]
  43. Hanai H, Mita Y, Hirogaki T, and Aoyama E (2024). Monitoring method of ball rolling motion with quaternion-based signal processing. Advances in Science and Technology, 143: 55–60. https://doi.org/10.4028/p-psCvO9   [Google Scholar]
  44. Hantrais-Gervois JL and Destarac D (2015). Drag polar invariance with flexibility. Journal of Aircraft, 52(3): 997–1001. https://doi.org/10.2514/1.C033193   [Google Scholar]
  45. Hay WW (2013). The nature of energy received from the sun: The analogies with water waves and sound. In: Hay WW (Ed.), Experimenting on a small planet: 180–207. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-642-28560-8_6   [Google Scholar]
  46. Hu D, Li R, Liu P, and Zhao J (2016). The design and influence of port arrangement on an improved wave rotor refrigerator performance. Applied Thermal Engineering, 107: 207–217. https://doi.org/10.1016/j.applthermaleng.2016.06.168   [Google Scholar]
  47. Huang Q, Zheng G, and Abbas M (2023). Data-driven solution for supersonic aerodynamics analysis of Perovskite solar cells considering the velocity of sound and Mach number. Mechanics of Advanced Materials and Structures, 31(27): 8832-8855. https://doi.org/10.1080/15376494.2023.2263445   [Google Scholar]
  48. Huda Z and Edi P (2013). Materials selection in design of structures and engines of supersonic aircrafts: A review. Materials and Design (1980-2015), 46: 552–560. https://doi.org/10.1016/j.matdes.2012.10.001   [Google Scholar]
  49. Hwang O, Lee MC, Weng W, Zhang Y, and Li Z (2019). Development of novel ultrasonic temperature measurement technology for combustion gas as a potential indicator of combustion instability diagnostics. Applied Thermal Engineering, 159: 113905. https://doi.org/10.1016/j.applthermaleng.2019.113905   [Google Scholar]
  50. Islas-Narvaez EA, Ituna-Yudonago JF, Ramos-Velasco LE, Vega-Navarrete MA, and Garcia-Salazar O (2022). Design and determination of aerodynamic coefficients of a tail-sitter aircraft by means of CFD numerical simulation. Machines, 11(1): 17. https://doi.org/10.3390/machines11010017   [Google Scholar]
  51. Jameel AT, Al-Qasaab MR, and Al-Naffakh J (2021). Decorative flame behavior study in visualizing wavelengths and frequency: Ruben's tube construction experiment. International Journal of Environment, Engineering and Education, 3(2): 41–47. https://doi.org/10.55151/ijeedu.v3i2.49   [Google Scholar]
  52. Javaid AY, Sun W, Devabhaktuni VK, and Alam M (2012). Cyber security threat analysis and modeling of an unmanned aerial vehicle system. In the IEEE Conference on Technologies for Homeland Security, IEEE, Waltham, USA: 585-590. https://doi.org/10.1109/THS.2012.6459914   [Google Scholar]
  53. Jung BK and Rezgui D (2023). Sectional leading edge vortex lift and drag coefficients of autorotating samaras. Aerospace, 10(5): 5. https://doi.org/10.3390/aerospace10050414   [Google Scholar]
  54. Kalakou S, Marques C, Prazeres D, and Agouridas V (2023). Citizens' attitudes towards technological innovations: The case of urban air mobility. Technological Forecasting and Social Change, 187: 122200. https://doi.org/10.1016/j.techfore.2022.122200   [Google Scholar]
  55. Kang R, Chanal H, Bonnemains T, Pateloup S, Branson DT, and Ray P (2012). Learning the forward kinematics behavior of a hybrid robot employing artificial neural networks. Robotica, 30(5): 847–855. https://doi.org/10.1017/S026357471100107X   [Google Scholar]
  56. Kaushik M (2022). Gas kinetics—Basic concepts. In: Kaushik M (Ed.), Fundamentals of gas dynamics: 1–46. Springer, Singapore, Singapore. https://doi.org/10.1007/978-981-16-9085-3_1   [Google Scholar]
  57. Khaji M, Degrez G, and van der Mullen J (2023). Self-consistent modeling of the flow-chemistry interplay in supersonically expanding CO2 mixtures; positive feedback of flow properties in supporting dissociation. Plasma Processes and Polymers, 20: e2200189. https://doi.org/10.1002/ppap.202200189   [Google Scholar]
  58. Kim JH, Mai TL, Cho A, Heo N, Yoon HK, Park JY, and Byun SH (2024). Establishment of a pressure variation model for the state estimation of an underwater vehicle. Applied Sciences, 14(3): 3. https://doi.org/10.3390/app14030970   [Google Scholar]
  59. Kitajima T, Akiyama K, Suzuki H, and Yasuno T (2024). Cloud distribution forecasting model using ground altitude information and CNN. In: Ma Y (Ed.), Progressive and integrative ideas and applications of engineering systems under the framework of IOT and AI: 134–145. Volume 1076, Springer Nature, Singapore, Singapore. https://doi.org/10.1007/978-981-99-6303-4_11   [Google Scholar]
  60. Kuprikov NM (2023). International standard atmosphere—A tool for technological measurement sovereignty in the aerospace industry. E3S Web of Conferences, 460: 07022. https://doi.org/10.1051/e3sconf/202346007022   [Google Scholar]
  61. Lamour R, März R, and Tischendorf C (2013). Differential-algebraic equations: A projector based analysis. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-642-27555-5   [Google Scholar]
  62. Laptev AM, Bram M, Garbiec D, Räthel J, van der Laan A, Beynet Y, Huber J, Küster M, Cologna M, and Guillon O (2024). Tooling in spark plasma sintering technology: Design, optimization, and application. Advanced Engineering Materials, 26: 2301391. https://doi.org/10.1002/adem.202301391   [Google Scholar]
  63. Levchenko MM and Levchenko MA (2023). Information technology procedures of error identification in metrological documents specifying the standard atmosphere parameters in terms of aircraft. Russian Aeronautics, 66: 182–192. https://doi.org/10.3103/S1068799823010257   [Google Scholar]
  64. Li C, Pan T, Yan Z, Zheng M, Li Q, and Dowell EH (2023). Aerodynamic characteristics of morphing supersonic cascade under low-upstream-Mach-number condition. AIAA Journal, 61(4): 1708–1719. https://doi.org/10.2514/1.J062563   [Google Scholar]
  65. Liu H, Luo Y, Liu H, and Hao C (2023). Grid gallop analysis using the Euler angle estimation method. In the 2nd International Conference on Smart Grids and Energy Systems, IEEE, Guangzhou, China: 214-217. https://doi.org/10.1109/SGES59720.2023.10366909   [Google Scholar]
  66. Lorenzetti JS, Bañuelos L, Clarke R, Murillo OJ, and Bowers A (2017). Determining products of inertia for small scale UAVs. In the 55th AIAA Aerospace Sciences Meeting, Grapevine, USA. https://doi.org/10.2514/6.2017-0547   [Google Scholar]
  67. Lu L (2010). Inverse modelling and inverse simulation for engineering applications. Lap Lambert Academic Publishing, Saarbrucken, Germany.   [Google Scholar]
  68. Lui HFS, Wolf WR, Ricciardi TR, and Gaitonde DV (2024). Mach number effects on shock-boundary layer interactions over curved surfaces of supersonic turbine cascades. Theoretical and Computational Fluid Dynamics, 38(4): 451–478. https://doi.org/10.1007/s00162-024-00712-2   [Google Scholar]
  69. Mahony JD (2013). Gauging the earth. The Mathematical Gazette, 97(540): 413–420. https://doi.org/10.1017/S0025557200000140   [Google Scholar]
  70. Marzouk OA (2008). A two-step computational aeroacoustics method applied to high-speed flows. Noise Control Engineering Journal, 56(5): 396-410. https://doi.org/10.3397/1.2978229   [Google Scholar]
  71. Marzouk OA (2009). Direct numerical simulations of the flow past a cylinder moving with sinusoidal and nonsinusoidal profiles. Journal of Fluids Engineering, 131(12): 121201. https://doi.org/10.1115/1.4000406   [Google Scholar]
  72. Marzouk OA (2010a). Characteristics of the flow-induced vibration and forces with 1- and 2-DOF vibrations and limiting solid-to-fluid density ratios. Journal of Vibration and Acoustics, 132(4): 041013. https://doi.org/10.1115/1.4001503   [Google Scholar]
  73. Marzouk OA (2010b). Contrasting the Cartesian and polar forms of the shedding-induced force vector in response to 12 subharmonic and superharmonic mechanical excitations. Fluid Dynamics Research, 42(3): 035507. https://doi.org/10.1088/0169-5983/42/3/035507   [Google Scholar]
  74. Marzouk OA (2011a). Flow control using bifrequency motion. Theoretical and Computational Fluid Dynamics, 25(6): 381–405. https://doi.org/10.1007/s00162-010-0206-6   [Google Scholar]
  75. Marzouk OA (2011b). One-way and two-way couplings of CFD and structural models and application to the wake-body interaction. Applied Mathematical Modelling, 35(3): 1036–1053. https://doi.org/10.1016/j.apm.2010.07.049   [Google Scholar]
  76. Marzouk OA (2017). Performance analysis of shell-and-tube dehydrogenation module: Dehydrogenation module. International Journal of Energy Research, 41(4): 604–610. https://doi.org/10.1002/er.3637   [Google Scholar]
  77. Marzouk OA (2018). Radiant heat transfer in nitrogen-free combustion environments. International Journal of Nonlinear Sciences and Numerical Simulation, 19(2): 175–188. https://doi.org/10.1515/ijnsns-2017-0106   [Google Scholar]
  78. Marzouk OA (2020). The Sod gasdynamics problem as a tool for benchmarking face flux construction in the finite volume method. Scientific African, 10: e00573. https://doi.org/10.1016/j.sciaf.2020.e00573   [Google Scholar]
  79. Marzouk OA (2022). Urban air mobility and flying cars: Overview, examples, prospects, drawbacks, and solutions. Open Engineering, 12(1): 662–679. https://doi.org/10.1515/eng-2022-0379   [Google Scholar]
  80. Marzouk OA and Nayfeh AH (2007). Mitigation of ship motion using passive and active anti-roll tanks. In the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, Las Vegas, USA, 48027: 215-229. https://doi.org/10.1115/DETC2007-35571   [Google Scholar]
  81. Marzouk OA and Nayfeh AH (2008a). A parametric study and optimization of ship-stabilization systems. In the 1st WSEAS International Conference on Maritime and Naval Science and Engineering, Valletta, Malta: 169–174.   [Google Scholar]
  82. Marzouk OA and Nayfeh AH (2008b). Hydrodynamic forces on a moving cylinder with time-dependent frequency variations. In the 46th AIAA Aerospace Sciences Meeting and Exhibit. https://doi.org/10.2514/6.2008-680   [Google Scholar] PMCid:PMC2645736
  83. Marzouk OA and Nayfeh AH (2009a). Control of ship roll using passive and active anti-roll tanks. Ocean Engineering, 36(9): 661–671. https://doi.org/10.1016/j.oceaneng.2009.03.005   [Google Scholar]
  84. Marzouk OA and Nayfeh AH (2009b). Reduction of the loads on a cylinder undergoing harmonic in-line motion. Physics of Fluids, 21(8): 083103. https://doi.org/10.1063/1.3210774   [Google Scholar]
  85. Marzouk OA and Nayfeh AH (2010). Characterization of the flow over a cylinder moving harmonically in the cross-flow direction. International Journal of Non-Linear Mechanics, 45(8): 821–833. https://doi.org/10.1016/j.ijnonlinmec.2010.06.004   [Google Scholar]
  86. Matsui M, Honjo N, Michishita K, and Yokoyama S (2023a). Characteristics of lightning discharges to wind turbines and weather conditions at upper air in winter in Japan. In the 12th Asia-Pacific International Conference on Lightning, IEEE, Langkawi, Malaysia: 1-6. https://doi.org/10.1109/APL57308.2023.10181380   [Google Scholar]
  87. Matsui M, Michishita K, and Yokoyama S (2023b). Influence of the −10 °C isotherm altitudes on winter lightning incidence at wind turbines in coastal areas of the Sea of Japan. Atmospheric Research, 296: 107071. https://doi.org/10.1016/j.atmosres.2023.107071   [Google Scholar]
  88. Matyja T, Stanik Z, and Kubik A (2023). Automatic correction of barometric altimeters using additional air temperature and humidity measurements. GPS Solutions, 28: 40. https://doi.org/10.1007/s10291-023-01582-7   [Google Scholar]
  89. Meku AA, Nageswara Rao DK, Mebratu MM, and Getnet LA (2023). Evaluation of the impact of wing span and wing chord length on the aerodynamic performance of Cessna 172-R aircraft. In: Woldegiorgis BH, Mequanint K, Getie MZ, Mulat EG, and Alemayehu Assegie A (Eds.), Advancement of science and technology: 419–434. Springer Nature, Cham, Switzerland. https://doi.org/10.1007/978-3-031-33610-2_24   [Google Scholar]
  90. Melnikov VG (2012). Inertia tensors and centres of masses identification at semiprogram precession motions. In the IEEE International Conference on Control Applications, IEEE, Dubrovnik, Croatia: 494-497. https://doi.org/10.1109/CCA.2012.6402471   [Google Scholar]
  91. Mi B and Zhan H (2020). Review of numerical simulations on aircraft dynamic stability derivatives. Archives of Computational Methods in Engineering, 27(5): 1515–1544. https://doi.org/10.1007/s11831-019-09370-8   [Google Scholar]
  92. Nandagopal NS (2023). Chemical thermodynamics. In: Nandagopal NS (Ed.), Chemical engineering principles and applications: 81–174. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-031-27879-2_2   [Google Scholar]
  93. Nandagopal NS (2024). Support areas: Thermodynamics. In: Nandagopal NS (Ed.), HVACR principles and applications: 85–125. Springer Nature, Cham, Switzerland. https://doi.org/10.1007/978-3-031-45267-3_3   [Google Scholar]
  94. Negahban MH, Bashir M, Traisnel V, and Botez RM (2024). Seamless morphing trailing edge flaps for UAS-S45 using high-fidelity aerodynamic optimization. Chinese Journal of Aeronautics, 37(2): 12–29. https://doi.org/10.1016/j.cja.2023.10.024   [Google Scholar]
  95. Oksuztepe E, Bayrak ZU, and Kaya U (2023). Effect of flight level to maximum power utilization for PEMFC/supercapacitor hybrid UAV with switched reluctance motor thruster. International Journal of Hydrogen Energy, 48(29): 11003–11016. https://doi.org/10.1016/j.ijhydene.2022.12.160   [Google Scholar]
  96. Orlov S (2018). Genesis of the Planet Earth. International Journal of Scientific Research in Civil Engineering, 2(5): 51–59.   [Google Scholar]
  97. Palit I, Janiuk A, and Sukova P (2019). Effects of adiabatic index on the sonic surface and time variability of low angular momentum accretion flows. Monthly Notices of the Royal Astronomical Society, 487(1): 755–768. https://doi.org/10.1093/mnras/stz1296   [Google Scholar]
  98. Pecora R (2021). Morphing wing flaps for large civil aircraft: Evolution of a smart technology across the Clean Sky program. Chinese Journal of Aeronautics, 34(7): 13–28. https://doi.org/10.1016/j.cja.2020.08.004   [Google Scholar]
  99. Prashantha BG, Seetharamu S, Narasimham GSVL, and Manjunatha K (2023). Effect of gas spacing and resonance frequency on theoretical performance of thermoacoustic refrigerators. International Journal of Air-Conditioning and Refrigeration, 31: 11. https://doi.org/10.1007/s44189-023-00027-7   [Google Scholar]
  100. Qiao G, Zhang T, and Barakos GN (2024). Numerical simulation of distributed propulsion systems using CFD. Aerospace Science and Technology, 147: 109011. https://doi.org/10.1016/j.ast.2024.109011   [Google Scholar]
  101. Qin Y, Liu P, Qu Q, and Guo H (2016). Numerical study of aerodynamic forces and flow physics of a delta wing in dynamic ground effect. Aerospace Science and Technology, 51: 203–221. https://doi.org/10.1016/j.ast.2016.02.007   [Google Scholar]
  102. Qu Q, Wang W, Liu P, and Agarwal RK (2015). Airfoil aerodynamics in ground effect for wide range of angles of attack. AIAA Journal, 53(4): 1048–1061. https://doi.org/10.2514/1.J053366   [Google Scholar]
  103. Randall R, Shkarayev S, Abate G, and Babcock J (2012). Longitudinal aerodynamics of rapidly pitching fixed-wing micro air vehicles. Journal of Aircraft, 49(2): 453–471. https://doi.org/10.2514/1.C031378   [Google Scholar]
  104. Raol JR and Singh J (2023). Flight mechanics modeling and analysis. 2nd Edition, CRC Press, Boca Raton, USA. https://doi.org/10.1201/9781003293514   [Google Scholar]
  105. Rizzi A (2011). Modeling and simulating aircraft stability and control—The SimSAC project. Progress in Aerospace Sciences, 47(8): 573–588. https://doi.org/10.1016/j.paerosci.2011.08.004   [Google Scholar]
  106. Rizzi SA, Letica SJ, Boyd DD, and Lopes LV (2024). Prediction of noise-power-distance data for urban air mobility vehicles. Journal of Aircraft, 61(1): 166–182. https://doi.org/10.2514/1.C037435   [Google Scholar]
  107. Rucker C and Wensing PM (2022). Smooth parameterization of rigid-body inertia. IEEE Robotics and Automation Letters, 7(2): 2771–2778. https://doi.org/10.1109/LRA.2022.3144517   [Google Scholar]
  108. Santana JJ, Ramos A, Rodriguez-Gonzalez A, Vasconcelos HC, Mena V, Fernández-Pérez BM, and Souto RM (2019). Shortcomings of international standard ISO 9223 for the classification, determination, and estimation of atmosphere corrosivities in subtropical archipelagic conditions—The case of the Canary Islands (Spain). Metals, 9(10): 1105. https://doi.org/10.3390/met9101105   [Google Scholar]
  109. Santos P, Sousa J, and Gamboa P (2017). Variable-span wing development for improved flight performance. Journal of Intelligent Material Systems and Structures, 28(8): 961–978. https://doi.org/10.1177/1045389X15595719   [Google Scholar]
  110. Scherllin‐Pirscher B, Steiner AK, Kirchengast G, Schwärz M, and Leroy SS (2017). The power of vertical geolocation of atmospheric profiles from GNSS radio occultation. Journal of Geophysical Research: Atmospheres, 122(3): 1595–1616. https://doi.org/10.1002/2016JD025902   [Google Scholar] PMid:28516029 PMCid:PMC5412943
  111. Secco NR and Mattos BSD (2017). Artificial neural networks to predict aerodynamic coefficients of transport airplanes. Aircraft Engineering and Aerospace Technology, 89(2): 211–230. https://doi.org/10.1108/AEAT-05-2014-0069   [Google Scholar]
  112. Simpson JG, Qin C, and Loth E (2023). Predicted roundtrip efficiency for compressed air energy storage using spray-based heat transfer. Journal of Energy Storage, 72: 108461. https://doi.org/10.1016/j.est.2023.108461   [Google Scholar]
  113. Smith MD and Richards C (2023). The influence of Mach number and overpressure on the structure of supersonic gas jets. Monthly Notices of the Royal Astronomical Society, 526(3): 3407–3420. https://doi.org/10.1093/mnras/stad2879   [Google Scholar]
  114. Song J, Kim T, and Song SJ (2012). Experimental determination of unsteady aerodynamic coefficients and flutter behavior of a rigid wing. Journal of Fluids and Structures, 29: 50–61. https://doi.org/10.1016/j.jfluidstructs.2011.12.009   [Google Scholar]
  115. Spedding GR and McArthur J (2010). Span efficiencies of wings at low Reynolds numbers. Journal of Aircraft, 47(1): 120–128. https://doi.org/10.2514/1.44247   [Google Scholar]
  116. Stankovic A and Müller WH (2024). An overview of methods for the description of rotations. In: Müller WH, Noe A, and Ferber F (Eds.), New achievements in mechanics: A tribute to Klaus Peter Herrmann: 425–439. Springer Nature, Cham, Switzerland. https://doi.org/10.1007/978-3-031-56132-0_18   [Google Scholar]
  117. Stengel RF (2022). Flight dynamics. 2nd Edition. Princeton University Press, Princeton, USA.   [Google Scholar]
  118. Stober G, Baumgarten K, McCormack JP, Brown P, and Czarnecki J (2020). Comparative study between ground-based observations and NAVGEM-HA analysis data in the mesosphere and lower thermosphere region. Atmospheric Chemistry and Physics, 20(20): 11979–12010. https://doi.org/10.5194/acp-20-11979-2020   [Google Scholar]
  119. Struchtrup H (2014). Thermodynamics and energy conversion. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-662-43715-5   [Google Scholar]
  120. Sun J, Hoekstra JM, and Ellerbroek J (2020). Estimating aircraft drag polar using open flight surveillance data and a stochastic total energy model. Transportation Research Part C: Emerging Technologies, 114: 391–404. https://doi.org/10.1016/j.trc.2020.01.026   [Google Scholar]
  121. Svozil K (2023). Early UFO sagas and legends prior to trinity (July 1945). In: Svozil K (Ed.), UFOs: Unidentified aerial phenomena: Observations, explanations and speculations: 3–13. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-031-34398-8_1   [Google Scholar]
  122. Tai S, Wang L, Wang Y, Bu C, and Yue T (2023). Flight dynamics modeling and aerodynamic parameter identification of four-degree-of-freedom virtual flight test. AIAA Journal, 61(6): 2652–2665. https://doi.org/10.2514/1.J062188   [Google Scholar]
  123. Tamesue K, Wen Z, Yamaguchi S, Kasai H, Kameyama W, Sato T, Katsuyama Y, Sato T, and Maesaka T (2023). A machine learning-based non-precipitating clouds estimation for THz dual-frequency radar. In the IEEE Conference on Antenna Measurements and Applications, IEEE, Genoa, Italy: 376-380. https://doi.org/10.1109/CAMA57522.2023.10352672   [Google Scholar]
  124. Tasca AL, Cipolla V, Abu Salem K, and Puccini M (2021). Innovative box-wing aircraft: Emissions and climate change. Sustainability, 13(6): 6. https://doi.org/10.3390/su13063282   [Google Scholar]
  125. Tewari A (2016). Flight of airplanes and gliders: Vertical plane. In: Tewari A (Ed.), Basic flight mechanics: 43–72. Springer International Publishing, Cham, Switzerland. https://doi.org/10.1007/978-3-319-30022-1_3   [Google Scholar]
  126. Thomas JW (2010). Numerical partial differential equations. Springer, Berlin, Germany.   [Google Scholar]
  127. Tian Y, Feng P, Liu P, Hu T, and Qu Q (2017). Spoiler upward deflection on transonic buffet control of supercritical airfoil and wing. Journal of Aircraft, 54(3): 1229–1233. https://doi.org/10.2514/1.C033574   [Google Scholar]
  128. Torenbeek E (2013). Advanced aircraft design: Conceptual design, analysis and optimization of subsonic civil airplanes. 1st Edition, Wiley, Hoboken, USA. https://doi.org/10.1002/9781118568101   [Google Scholar]
  129. Voet LJA, Prashanth P, Speth RL, Sabnis JS, Tan CS, and Barrett SRH (2024). Reduced-order model for supersonic transport takeoff noise scaling with cruise Mach number. Journal of Aircraft, 61(4): 1155–1168. https://doi.org/10.2514/1.C037633   [Google Scholar]
  130. Wang H, Jiang X, Chao Y, Li Q, Li M, Zheng W, and Chen T (2019). Effects of leading edge slat on flow separation and aerodynamic performance of wind turbine. Energy, 182: 988–998. https://doi.org/10.1016/j.energy.2019.06.096   [Google Scholar]
  131. Wang X and Cai L (2015). Mathematical modeling and control of a tilt-rotor aircraft. Aerospace Science and Technology, 47: 473–492. https://doi.org/10.1016/j.ast.2015.10.012   [Google Scholar]
  132. Woody AI (2013). How is the ideal gas law explanatory? Science and Education, 22(7): 1563–1580. https://doi.org/10.1007/s11191-011-9424-6   [Google Scholar]
  133. Xu X and Lagor FD (2021). Quasi-steady effective angle of attack and its use in lift-equivalent motion design. AIAA Journal, 59(7): 2613–2626. https://doi.org/10.2514/1.J059663   [Google Scholar]
  134. Young M (2020). Capital, class and the social necessity of passenger air transport. Progress in Human Geography, 44(5): 938–958. https://doi.org/10.1177/0309132519888680   [Google Scholar]
  135. Yuan P, Zhang M, Jiang W, Awange J, Mayer M, Schuh H, and Kutterer H (2024). Chapter 10—GNSS application for weather and climate change monitoring. In: Aoki Y and Kreemer C (Eds.), GNSS monitoring of the terrestrial environment: 189–204. Elsevier, Amsterdam, Netherlands. https://doi.org/10.1016/B978-0-323-95507-2.00006-2   [Google Scholar]
  136. Zajdel A, Krawczyk M, and Szczepański C (2022). Pre-flight test verification of automatic stabilization system using aircraft trimming surfaces. Aerospace, 9(2): 111. https://doi.org/10.3390/aerospace9020111   [Google Scholar]
  137. Zajdel A, Krawczyk M, and Szczepański C (2023). Trim tab flight stabilisation system performance assessment under degraded actuator speeds. Aerospace, 10(5): 429. https://doi.org/10.3390/aerospace10050429   [Google Scholar]
  138. Zamuraev VP and Kalinina AP (2023). Combustion of kerosene in a supersonic flow at Mach number m = 1.7 under the action of gas-dynamical pulses. Journal of Engineering Physics and Thermophysics, 96(4): 906–912. https://doi.org/10.1007/s10891-023-02752-7   [Google Scholar]
  139. Zhang F and Graham DJ (2020). Air transport and economic growth: A review of the impact mechanism and causal relationships. Transport Reviews, 40(4): 506–528. https://doi.org/10.1080/01441647.2020.1738587   [Google Scholar]
  140. Zhang JH and Yao ZX (2013). Optimized explicit finite-difference schemes for spatial derivatives using maximum norm. Journal of Computational Physics, 250: 511–526. https://doi.org/10.1016/j.jcp.2013.04.029   [Google Scholar]
  141. Zheng C, Jin Z, Dong Q, and Yang Z (2024). Numerical investigation of the influences of ridge ice parameters on lift and drag coefficients of airfoils through design of experiments. Advances in Mechanical Engineering, 16(1). https://doi.org/10.1177/16878132231226056   [Google Scholar]
  142. Zhou W and Wang H (2015). Researches on inverse simulation's applications in teleoperation rendezvous and docking based on hyper-ellipsoidal restricted model predictive control for inverse simulation structure. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 229(9): 1675–1689. https://doi.org/10.1177/0954410014558320   [Google Scholar]