DROMO propagator revisited

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• 作者：Hodei Urrutxua ; Manuel Sanjurjo-Rivo…
• 关键词：DROMO ; Hansen’s ideal frame ; Regularization ; Orbit propagation ; Euler ; Rodrigues parameters ; Quaternions ; Earth’s satellites
• 刊名：Celestial Mechanics & Dynamical Astronomy
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：124
• 期：1
• 页码：1-31
• 全文大小：1,152 KB
• 参考文献：Awad, M.: Oblateness and drag effects on the motion of satellites in the set of Eulerian redundant parameters. Earth Moon Planets 62(2), 161–177 (1993)MathSciNet CrossRef ADS
  Awad, M.: Analytical solution to the perturbed \(j_2\) motion of artificial satellite in terms of Euler parameters. Earth Moon Planets 69(1), 1–12 (1995)MATH CrossRef ADS
  Barrio, R., Serrano, S.: Performance of perturbation methods on orbit prediction. Math. Comput. Model. 48(3), 594–600 (2008)MATH MathSciNet CrossRef
  Baù, G., Bombardelli, C.: Time elements for enhanced performance of the DROMO orbit propagator. Astron. J. 148(3), 43 (2014). doi:10.​1088/​0004-6256/​148/​3/​43 CrossRef ADS
  Baù, G., Bombardelli, C., Peláez, J.: Adaptive scheme for accurate orbit propagation. J. Aerosp. Eng. Sci. Appl. 15(35), 131 (2010)
  Baù, G., Bombardelli, C., Peláez, J.: A new set of integrals of motion to propagate the perturbed two-body problem. Celest. Mech. Dyn. Astron. 116(1), 53–78 (2013). doi:10.​1007/​s10569-013-9475-x MATH CrossRef ADS
  Berry, M.M.: A variable-step double-integration multi-step integrator. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia (2004)
  Bond, V.R., Allman, M.C.: Modern Astrodynamics: Fundamentals and Perturbation Methods. Princeton University Press, Princeton (1996)
  Broucke, R., Lass, H.: On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization. Celest. Mech. 12(3), 317–325 (1975)MATH MathSciNet CrossRef ADS
  Cid, R., San Saturio, M.: Motion of rigid bodies in a set of redundant variables. Celest. Mech. 42(1), 263–277 (1987)MATH MathSciNet CrossRef ADS
  Danby, J.: Fundamentals of Celestial Mechanics, vol. 1. Willmann-Bell, Inc, Richmond (1992)
  Deprit, A.: Ideal elements for perturbed Keplerian motions. J. Res. Natl. Bur. Stand. Sect. B Math. Sci. 79B(1–2):1–15 (1975) (paper 79B1&2–416)
  Deprit, A.: Ideal frames for perturbed Keplerian motions. Celest. Mech. 13(2), 253–263 (1976)MATH MathSciNet CrossRef ADS
  Efroimsky, M., Goldreich, P.: Gauge freedom in the n-body problem of celestial mechanics. Astron. Astrophys. 415(3), 1187–1199 (2004)MATH CrossRef ADS
  Esteban-Dones, J., Peláez, J.: Advanced propagation of interplanetary orbits in the exploration of jovian moons. In: 4th International Conference on Astrodynamics Tools and Techniques, pp. 3–6 (2010a)
  Esteban-Dones, J., Peláez, J.: Advanced propagation of interplanetary orbits in the exploration of jovian moons. In: 5th International Workshop and Advanced School “Spaceflight Dynamics and Control”, 17–19 March 2010, Covilha, Portugal (2010b)
  Fehlberg, E.: Classical fifth-, sixth-, seventh-, and eighth-order Runge–Kutta formulas with stepsize control. Nasa tr r-287, George C. Marshall Space Flight Center, Huntsville, Alabama (1968)
  Gómez, J.L.G.: Perturbation methods in optimal control problems applied to low thrust space trajectories. Master’s thesis, ETSI Aeronáuticos, Technical University of Madrid (UPM) (2012)
  Hansen, P.A.: Auseinandersetzung einer zweckmässigen mmethod zur berechnung der absoluten störungen der kleinen planeten. Abh der Math-Phys Cl der Kon Sachs Ges der Wissensch 5, 41–218 (1857)
  Hintz, G.: Survey of orbit element sets. J. Guid. Control Dyn. 31(3), 785–790 (2008)CrossRef ADS
  Hughes, P.C.: Spacecraft Attitude Dynamics. Dover Books on Aeronautical Engineering. Dover Publications, New York (2004)
  Janin, G.: Accurate computation of highly eccentric satellite orbits. Celest. Mech. 10, 451–467 (1974). doi:10.​1007/​BF01229121 MATH CrossRef ADS
  Palacios, M., Calvo, C.: Quaternions formulation versus regularization in numerical orbit computation. Astrodynamics 1993, 2629–2644 (1993)
  Palacios, M., Calvo, C.: Ideal frames and regularization in numerical orbit computation. J. Astron. Sci. 44(1), 63–77 (1996)
  Palacios, M., Abad, A., Elipe, A.: An efficient numerical method for orbit computations. In: Astrodynamics 1991, vol. 1, pp. 265–274 (1992)
  Peláez, J., Hedo, J.M.: Un método de perturbaciones especiales en dinámica de tethers. Monografías de la Real Academia de Ciencias de Zaragoza 22, 119–140 (2003)
  Peláez, J., Hedo, J.M., Rodriguez, P.: A special perturbation method in orbital dynamics. In: Vallado, D.A., Gabor, M.J., Desai, P.N. (eds.) AAS/AIAA Spaceflight Mechanics Meeting 2005, Advances in the Astronautical Sciences, vol. 120, pp. 1061–1078 (2005)
  Peláez, J., Hedo, J.M., de Andrés, P.R.: A special perturbation method in orbital dynamics. Celest. Mech. Dyn. Astron. 97, 131–150 (2007). doi:10.​1007/​s10569-006-9056-3 MATH CrossRef ADS
  Prince, P., Dormand, J.: High order embedded Runge–Kutta formulae. J. Comput. Appl. Math. 7(1), 67–75 (1981). doi:10.​1016/​0771-050X(81)90010-3 MATH MathSciNet CrossRef
  Roa, J., Sanjurjo-Rivo, M., Peláez, J.: Singularities in DROMO formulation. Analysis of deep flybys. Adv. Space Res. (2015). doi:10.​1016/​j.​asr.​2015.​03.​019
  Shampine, L., Gordon, M.: Computer Solution of Ordinary Differential Equations. W. H. Freeman and Company, San Francisco (1975)MATH
  Sharaf, M., Awad, M., Najmuldeen, S.: The motion of artificial satellites in the set of Eulerian redundant parameters. Earth Moon Planets 55(1), 21–44 (1991a)MATH CrossRef ADS
  Sharaf, M., Awad, M., Najmuldeen, S.: Motion of artificial satellites in the set of Eulerian redundant parameters, II. Earth Moon Planets 55(3), 223–231 (1991b)MATH CrossRef ADS
  Sharaf, M., Awad, M., Najmuldeen, S.: Motion of artificial satellites in the set of Eulerian redundant parameters (III). Earth Moon Planets 56(2), 141–164 (1992)MATH CrossRef ADS
  Shuster, M.D.: A survey of attitude representations. J. Astron. Sci. 41(4), 439–517 (1993)MathSciNet
  Stiefel, E., Scheifele, G.: Linear and Regular Celestial Mechanics. Springer, Berlin (1971)MATH CrossRef
  Urrutxua, H., Morante, D., Sanjurjo-Rivo, M., Peláez, J.: DROMO formulation for planar motion: solution to the Tsien problem. Celest. Mech. Dyn. Astron. 122(2), 143–168 (2015). doi:10.​1007/​s10569-015-9613-8 CrossRef ADS
  Velez, C., Hilinski, S.: Time transformations and Cowell’s method. Celest. Mech. 17(1), 83–99 (1978). doi:10.​1007/​BF01261054 MATH CrossRef ADS
  
• 作者单位：Hodei Urrutxua (1)
  Manuel Sanjurjo-Rivo (2)
  Jesús Peláez (1)
  
  1. Space Dynamics Group (SDG-UPM), Technical University of Madrid, Pza. Cardenal Cisneros 3, 28040, Madrid, Spain
  2. Space Dynamics Group (SDG-UPM), Bioengineering and Aerospace Engineering Department, Carlos III University, Avda. de la Universidad 30, 28911, Leganés, Madrid, Spain
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Astronomy
  Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9478

文摘

In the year 2000 an in-house orbital propagator called DROMO (Peláez et al. in Celest Mech Dyn Astron 97:131–150, 2007. doi:10.​1007/​s10569-006-9056-3) was developed by the Space Dynamics Group of the Technical University of Madrid, based in a set of redundant variables including Euler–Rodrigues parameters. An original deduction of the DROMO propagator is carried out, underlining its close relation with the ideal frame concept introduced by Hansen (Abh der Math-Phys Cl der Kon Sachs Ges der Wissensch 5:41–218, 1857). Based on the very same concept, Deprit (J Res Natl Bur Stand Sect B Math Sci 79B(1–2):1–15, 1975) proposed a formulation for orbit propagation. In this paper, similarities and differences with the theory carried out by Deprit are analyzed. Simultaneously, some improvements are introduced in the formulation, that lead to a more synthetic and better performing propagator. Also, the long-term effect of the oblateness of the primary is studied in terms of DROMO variables, and new numerical results are presented to evaluate the performance of the method. Keywords DROMO Hansen’s ideal frame Regularization Orbit propagation Euler-Rodrigues parameters Quaternions Earth’s satellites