Abstract
The definition of Hansen coefficient \(X_{k}^{n,m}\) is (Plummer in An introductory treatise on dynamical astronomy, Cambridge University Press, London, 1918).
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References
Plummer HC (1918) An introductory treatise on dynamical astronomy. Cambridge University Press, London
Laskar J, Boué G (2010) Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations. Astron Astrophys 522:A60
Wu LD (2011) Orbit and detection of artificial satellites and space debris. China Science and Technology Press, Beijing (In Chinese)
McClain WD (1978) A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume II. the explicit development of the first-order averaged equations of motion for the nonspherical gravitational and nonresonant third-body perturbations. NASA CR-156783
Cook GE (1973) Basic theory for PROD, a program for computing the development of satellite orbits. Celest Mech 7(3):301–314
Laskar J (2005) Note on the generalized Hansen and Laplace coefficients. Celest Mech Dyn Astron 91(3–4):351–356
Hansen PA (1855) Entwickelung der products einer potenz des radius vectors mit dem sinus oder cosinus eines vielfachen der wahren anomalie in reihen, Abhandl. d. K. S. Ges. d. Wissensch, vol IV, pp 182–281
Giacaglia GEO (1976) A note on Hansen’s coefficients in satellite theory. Celest Mech 14(4):515–523
Wu LD, Wang HB, Ma JY (2012) Inclination function in satellite dynamics. Science Press, Beijing
Wu LD, Zhang MJ (2012) Recursive methods for computation of Hansen coefficients \(X_{0}^{n,m}, X_{0}^{-(n+1),m}\) and their derivatives. J Astrodyn 2(4):1–10 (In Chinese)
Kaula WM (1961) Analysis of gravitational and geometric aspects of geodetic utilization of satellites. Geophys J Int 5(2):104–133
Kaula WM (1962) Development of the lunar and solar disturbing function for a close satellite. Astron J 67(5):300–303
Vakhidov AA (2001) Some recurrence relations between Hansen coefficients. Celest Mech Dyn Astron 81(3):177–190
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Wu, L., Zhang, M. (2024). Calculation of \(X_{0}^{n,m}\) and \(X_{0}^{{ - \left( {n + 1} \right),m}}\) and Their Derivatives. In: Hansen Coefficients in Satellite Orbital Dynamics. Springer Aerospace Technology. Springer, Singapore. https://doi.org/10.1007/978-981-97-0456-9_2
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DOI: https://doi.org/10.1007/978-981-97-0456-9_2
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