Complex variables approach to the short-axis-mode rotation of a rigid body

[1]E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 2nd Edition, Cambridge University Press, 1917.WhittakerE. T.A Treatise on the Analytical Dynamics of Particles and Rigid Bodies2ndCambridge University Press1917Search in Google Scholar

[2]V. Golubev, Lectures on Integration of the Equations of Motion of a Rigid Body about a Fixed Point, Israel Program for Scientific Translations, S. Monson, Jerusalem, 1960.GolubevV.Lectures on Integration of the Equations of Motion of a Rigid Body about a Fixed PointIsrael Program for Scientific TranslationsS. MonsonJerusalem1960Search in Google Scholar

[3]M. H. Andoyer, Cours de mécanique céleste. Tome I., Paris: Gauthier-Villars, 438 S. (1923).AndoyerM. H.Cours de mécanique célesteTomeI.ParisGauthier-Villars4381923Search in Google Scholar

[4]A. Deprit, Free rotation of a rigid body studied in the phase space, American Journal of Physics 35 (1967) 424–428.DepritA.Free rotation of a rigid body studied in the phase spaceAmerican Journal of Physics35196742442810.1119/1.1974113Search in Google Scholar

[5]M. Lara, S. Ferrer, Expanding the simple pendulum’s rotation solution in action-angle variables, European Journal of Physics 36 (5) (2015) 055040. doi:10.1088/0143-0807/36/5/055040.LaraM.FerrerS.Expanding the simple pendulum’s rotation solution in action-angle variablesEuropean Journal of Physics3652015055040doi:10.1088/0143-0807/36/5/055040Open DOISearch in Google Scholar

[6]M. Lara, S. Ferrer, Expanding the simple pendulum’s rotation solution in action-angle variables, ArXiv e-prints arXiv:1503.03358.LaraM.FerrerS.Expanding the simple pendulum’s rotation solution in action-angle variablesArXiv e-printsarXiv:1503.0335810.1088/0143-0807/36/5/055040Search in Google Scholar

[7]H. Kinoshita, First-Order Perturbations of the Two Finite Body Problem, Publications of the Astronomical Society of Japan 24 (1972) 423–457.KinoshitaH.First-Order Perturbations of the Two Finite Body ProblemPublications of the Astronomical Society of Japan241972423457Search in Google Scholar

[8]H. Kinoshita, Analytical expansions of torque-free motions for short and long axis modes, Celestial Mechanics and Dynamical Astronomy 53 (4) (1992) 365–375. doi:10.1007/BF00051817.KinoshitaH.Analytical expansions of torque-free motions for short and long axis modesCelestial Mechanics and Dynamical Astronomy5341992365375doi:10.1007/BF00051817Open DOISearch in Google Scholar

[9]A. Escapa, J. Getino, J. M. Ferrándiz, Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations, Astronomy & Astrophysics 389 (2002) 1047–1054. doi:10.1051/0004-6361:20020734.EscapaA.GetinoJ.FerrándizJ. M.Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations, Astronomy & Astrophysics389200210471054doi:10.1051/0004-636120020734Open DOISearch in Google Scholar

[10]J. Souchay, M. Folgueira, S. Bouquillon, Effects of the Triaxiality on the Rotation of Celestial Bodies: Application to the Earth, Mars and Eros, Earth Moon and Planets 93 (2) (2003) 107–144. doi:10.1023/B:MOON.0000034505.79534.01.SouchayJ.FolgueiraM.BouquillonS.Effects of the Triaxiality on the Rotation of Celestial Bodies: Application to the Earth, Mars and Eros, Earth Moon and Planets9322003107144doi:10.1023/B:MOON.0000034505.79534.01Open DOISearch in Google Scholar

[11]S. Ferrer, M. Lara, Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor, The Astronomical Journal 139 (5) (2010) 1899–1908. doi:10.1088/0004-6256/139/5/1899.FerrerS.LaraM.Integration of the Rotation of an Earth-like Body as a Perturbed Spherical RotorThe Astronomical Journal1395201018991908doi:10.1088/0004-6256/139/5/1899Open DOISearch in Google Scholar

[12]M. Lara, Short-axis-mode rotation of a free rigid body by perturbation series, Celestial Mechanics and Dynamical Astronomy 118 (3) (2014) 221–234. doi:10.1007/s10569-014-9532-0.LaraM.Short-axis-mode rotation of a free rigid body by perturbation seriesCelestial Mechanics and Dynamical Astronomy11832014221234doi:10.1007/s10569-014-9532-0Open DOISearch in Google Scholar

[13]M. Lara, T. Fukushima, S. Ferrer, Ceres’ rotation solution under the gravitational torque of the Sun, Monthly Notices of the Royal Astronomical Society 415 (1) (2011) 461–469. doi:10.1111/j.1365-2966.2011.18717.x.LaraM.FukushimaT.FerrerS.Ceres’ rotation solution under the gravitational torque of the SunMonthly Notices of the Royal Astronomical Society41512011461469doi:10.1111/j.1365-2966.2011.18717.xOpen DOISearch in Google Scholar

[14]M. C. Zanardi, Study of the terms of coupling between rotational and translational motions, Celestial Mechanics 39 (1) (1986) 147–158. doi:10.1007/BF01230847.ZanardiM. C.Study of the terms of coupling between rotational and translational motionsCelestial Mechanics3911986147158doi:10.1007/BF01230847Open DOISearch in Google Scholar

[15]J.-M. Ferrándiz, M.-E. Sansaturio, Elimination of the nodes when the satellite is a non spherical rigid body, Celestial Mechanics and Dynamical Astronomy 46 (4) (1989) 307–320. doi:10.1007/BF00051485.FerrándizJ.-M.SansaturioM.-E.Elimination of the nodes when the satellite is a non spherical rigid bodyCelestial Mechanics and Dynamical Astronomy4641989307320doi:10.1007/BF00051485Open DOISearch in Google Scholar

[16]M. Lara, T. Fukushima, S. Ferrer, First-order rotation solution of an oblate rigid body under the torque of a perturber in circular orbit, Astronomy & Astrophysics 519 (2010) A1. doi:10.1051/0004-6361/200913880.LaraM.FukushimaT.FerrerS.First-order rotation solution of an oblate rigid body under the torque of a perturber in circular orbitAstronomy & Astrophysics5192010A1doi:10.1051/0004-6361/200913880Open DOISearch in Google Scholar

[17]J. Getino, J. M. Ferrándiz, A. Escapa, Hamiltonian theory for the non-rigid Earth: Semidiurnal terms, Astronomy & Astrophysics 370 (2001) 330–341. doi:10.1051/0004-6361:20010186.GetinoJ.FerrándizJ. M.EscapaA.Hamiltonian theory for the non-rigid Earth: Semidiurnal terms, Astronomy & Astrophysics3702001330341doi:10.1051/0004-636120010186Open DOISearch in Google Scholar

[18]S. Ferrer, C. A. Williams, Simplifications toward Integrability of Perturbed Keplerian Systems, Annals of the New York Academy of Sciences 536 (1988) 127–139. doi:10.1111/j.1749-6632.1988.tb51569.x.FerrerS.WilliamsC. A.Simplifications toward Integrability of Perturbed Keplerian SystemsAnnals of the New York Academy of Sciences5361988127139doi:10.1111/j.1749-6632.1988.tb51569.xOpen DOISearch in Google Scholar

[19]A. Deprit, S. Ferrer, Simplifications in the theory of artificial satellites, Journal of the Astronautical Sciences 37 (4) (1989) 451–463.DepritA.FerrerS.Simplifications in the theory of artificial satellitesJournal of the Astronautical Sciences3741989451463Search in Google Scholar

[20]V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd Edition, Springer-Verlag, New York, 1989.ArnoldV. I.Mathematical Methods of Classical Mechanics2ndSpringer-VerlagNew York198910.1007/978-1-4757-2063-1Search in Google Scholar

[21]S. Ferrer, M. Lara, Families of Canonical Transformations by Hamilton-Jacobi-Poincaré Equation. Application to Rotational and Orbital Motion, Journal of Geometric Mechanics 2 (3) (2010) 223–241. doi:10.3934/jgm.2010.2.223.FerrerS.LaraM.Families of Canonical Transformations by Hamilton-Jacobi-Poincaré EquationApplication to Rotational and Orbital Motion, Journal of Geometric Mechanics232010223241doi:10.3934/jgm.2010.2.223Open DOISearch in Google Scholar

[22]J. Henrard, Virtual singularities in the artificial satellite theory, Celestial Mechanics 10 (4) (1974) 437–449. doi:10.1007/BF01229120.HenrardJ.Virtual singularities in the artificial satellite theoryCelestial Mechanics1041974437449doi:10.1007/BF01229120Open DOISearch in Google Scholar

[23]R. H. Lyddane, Small eccentricities or inclinations in the Brouwer theory of the artificial satellite, Astronomical Journal 68 (8) (1963) 555–558. doi:10.1086/109179.LyddaneR. H.Small eccentricities or inclinations in the Brouwer theory of the artificial satelliteAstronomical Journal6881963555558doi:10.1086/109179Open DOISearch in Google Scholar

[24]A. Deprit, A. Rom, The Main Problem of Artificial Satellite Theory for Small and Moderate Eccentricities, Celestial Mechanics 2 (2) (1970) 166–206.DepritA.RomA.The Main Problem of Artificial Satellite Theory for Small and Moderate EccentricitiesCelestial Mechanics22197016620610.1007/BF01229494Search in Google Scholar

[25]M. Lara, Efficient Formulation of the Periodic Corrections in Brouwer’s Gravity Solution, Mathematical Problems in Engineering vol. 2015 (Article ID 980652) (2015) 1–9. doi:10.1155/2015/980652.LaraM.Efficient Formulation of the Periodic Corrections in Brouwer’s Gravity SolutionMathematical Problems in Engineering2015Article ID 980652201519doi:10.1155/2015/980652Open DOISearch in Google Scholar

[26]D. Hautesserres, M. Lara, Intermediary LEO propagation including higher order zonal harmonics, Celestial Mechanics and Dynamical Astronomy 127 (2017) 505–526. arXiv:1605.00525, doi:10.1007/s10569-016-9736-6.HautesserresD.LaraM.Intermediary LEO propagation including higher order zonal harmonicsCelestial Mechanics and Dynamical Astronomy1272017505526arXiv:1605.00525doi:10.1007/s10569-016-9736-6Open DOISearch in Google Scholar

[27]T. Fukushima, New Canonical Variables for Orbital and Rotational Motions, in: H. Kinoshita, H. Nakai (Eds.), 25th Symposium on Celestial Mechanics,, 1992, p. 100.FukushimaT.New Canonical Variables for Orbital and Rotational MotionsKinoshitaH.NakaiH.25th Symposium on Celestial Mechanics1992100Search in Google Scholar

[28]T. Fukushima, New canonical variables for orbital and rotational motions, Celestial Mechanics and Dynamical Astronomy 60 (1994) 57–68. doi:10.1007/BF00693092.FukushimaT.New canonical variables for orbital and rotational motionsCelestial Mechanics and Dynamical Astronomy6019945768doi:10.1007/BF00693092Open DOISearch in Google Scholar

[29]A. Deprit, A Transformation Due to Fukushima (Invited Papers), in: K. Kurzynska, F. Barlier, P. K. Seidelmann, I. Wyrtrzyszczak (Eds.), Dynamics and Astrometry of Natural and Artificial Celestial Bodies, 1994, p. 159.DepritA.A Transformation Due to Fukushima (Invited Papers)KurzynskaK.BarlierF.SeidelmannP. K.WyrtrzyszczakI.Dynamics and Astrometry of Natural and Artificial Celestial Bodies1994p. 159Search in Google Scholar

[30]J. Henrard, M. Moons, Hamiltonian Theory of the Libration of the Moon, in: V. G. Szebehely (Ed.), Dynamics of planets and satellites and theories of their motion, Vol. 72 of Astrophysics and Space Science Library, Proceedings of the International Astronomical Union colloquium no. 41, D. Reidel Publishing Company, Dordrecht: Holland / Boston: U.S.A., 1978, pp. 125–135.HenrardJ.MoonsM.Hamiltonian Theory of the Libration of the MoonSzebehelyV. G.Dynamics of planets and satellites and theories of their motion, Vol. 72 of Astrophysics and Space Science Library, Proceedings of the International Astronomical Union colloquium no. 41D. Reidel Publishing Company, DordrechtHolland / Boston: U.S.A.1978125135Search in Google Scholar

[31]M. Kummer, On resonant non linearly coupled oscillators with two equal frequencies, Communications in Mathematical Physics 48 (1976) 53–79. doi:10.1007/BF01609411.KummerM.On resonant non linearly coupled oscillators with two equal frequenciesCommunications in Mathematical Physics4819765379doi:10.1007/BF01609411Open DOISearch in Google Scholar

[32]A. Giorgilli, L. Galgani, Formal integrals for an autonomous Hamiltonian system near an equilibrium point, Celestial Mechanics 17 (1978) 267–280. doi:10.1007/BF01232832.GiorgilliA.GalganiL.Formal integrals for an autonomous Hamiltonian system near an equilibrium pointCelestial Mechanics171978267280doi:10.1007/BF01232832Open DOISearch in Google Scholar

[33]M. Lara, I. Pérez, R. López, Higher Order Approximation to the Hill Problem Dynamics about the Libration Points, Communications in Nonlinear Science and Numerical Simulation in press. doi:10.1016/j.cnsns.2017.12.007.LaraM.PérezI.LópezR.Higher Order Approximation to the Hill Problem Dynamics about the Libration PointsCommunications in Nonlinear Science and Numerical Simulation in pressdoi:10.1016/j.cnsns.2017.12.007Open DOISearch in Google Scholar

[34]D. L. Hitzl, J. V. Breakwell, Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite., Celestial Mechanics 3 (5) (1971) 346–383. doi:10.1007/BF01231806.HitzlD. L.BreakwellJ. V.Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satelliteCelestial Mechanics351971346383doi:10.1007/BF01231806Open DOISearch in Google Scholar

[35]M. Lara, S. Ferrer, Closed form perturbation solution of a fast rotating triaxial satellite under gravity-gradient torque, Cosmic Research 51 (4) (2013) 289–303. doi:10.1134/S0010952513040059.LaraM.FerrerS.Closed form perturbation solution of a fast rotating triaxial satellite under gravity-gradient torqueCosmic Research5142013289303doi:10.1134/S0010952513040059Open DOISearch in Google Scholar

[36]N. Hatten, R. P. Russell, Semianalytical Technique for Six-Degree-of-Freedom Space Object Propagation, Journal of Guidance, Control, and Dynamics, on line (2018) 12p. doi:10.2514/1.G003706.HattenN.RussellR. P.Semianalytical Technique for Six-Degree-of-Freedom Space Object PropagationJournal of Guidance, Control, and Dynamics, on line201812pdoi:10.2514/1.G003706Open DOISearch in Google Scholar

[37]J. M. Ferrándiz, J. F. Navarro, A. Escapa, J. Getino, Earth’s Rotation: A Challenging Problem in Mathematics and Physics, Pure and Applied Geophysics 172 (2015) 57–74. doi:10.1007/s00024-014-0879-7.FerrándizJ. M.NavarroJ. F.EscapaA.GetinoJ.Earth’s Rotation: A Challenging Problem in Mathematics and PhysicsPure and Applied Geophysics17220155774doi:10.1007/s00024-014-0879-7Open DOISearch in Google Scholar

[38]Y. A. Sadov, The Action-Angles Variables in the Euler-Poinsot Problem, PMM-Journal of Applied Mathematics and Mechanics 34 (5) (1970) 922–925.SadovY. A.The Action-Angles Variables in the Euler-Poinsot ProblemPMM-Journal of Applied Mathematics and Mechanics345197092292510.1016/0021-8928(70)90077-8Search in Google Scholar

[39]P. F. Byrd, M. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, 2nd Edition, Springer-Verlag, Berlin, Heidelberg and New York, 1971.ByrdP. F.FriedmanM.Handbook of Elliptic Integrals for Engineers and Physicists2ndSpringer-VerlagBerlin, Heidelberg and New York197110.1007/978-3-642-65138-0Search in Google Scholar

[40]H. Goldstein, C. P. Poole, J. L. Safko, Classical Mechanics, 3rd Edition, Addison-Wesley, 2001.GoldsteinH.PooleC. P.SafkoJ. L.Classical Mechanics3rdAddison-Wesley200110.1119/1.1484149Search in Google Scholar

[41]A. Deprit, Canonical transformations depending on a small parameter, Celestial Mechanics 1 (1) (1969) 12–30. doi:10.1007/BF01230629.DepritA.Canonical transformations depending on a small parameterCelestial Mechanics1119691230doi:10.1007/BF01230629Open DOISearch in Google Scholar

[42]K. R. Meyer, G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer, New York, 1992.MeyerK. R.HallG. R.Introduction to Hamiltonian Dynamical Systems and the N-Body ProblemSpringerNew York199210.1007/978-1-4757-4073-8Search in Google Scholar

[43]D. Boccaletti, G. Pucacco, Theory of orbits. Volume 2: Perturbative and geometrical methods, 1st Edition, Astronomy and Astrophysics Library, Springer-Verlag, Berlin Heidelberg New York, 2002.BoccalettiD.PucaccoG.Theory of orbits2Perturbative and geometrical methods1stAstronomy and Astrophysics Library, Springer-VerlagBerlin Heidelberg New York2002Search in Google Scholar