[1]

ROSSI, A. “Resonant dynamics of Medium Earth Orbits: Space Debris Issues,”

*Celestial Mechanics and Dynamical Astronomy*, Vol. 100, No. 4, 2008, pp. 267–286.

MathSciNetMATHCrossRefGoogle Scholar[2]

ANSELMO, L. and PARDINI, C., “Long-Term Dynamical Evolution of High Area-to-Mass Ratio Debris Released into High Earth Orbits,”

*Acta Astronautica*, Vol. 67, 2010, pp. 204–216.

CrossRefGoogle Scholar[3]

ANSELMO, L. and PARDINI, C. “Dynamical Evolution of High Area-to-Mass Ratio Debris Released into GPS Orbits,”

*Advances in Space Research*, Vol. 43, 2009, pp. 1491–1508.

CrossRefGoogle Scholar[4]

ELY, T.A. and HOWELL, K.C. “Long Term Evolution of Artificial Satellite Orbits due to Resonant Tesseral Harmonics,” The

*Journal of the Astronautical Sciences* Vol. 44, 1996, pp. 167–190.

Google Scholar[5]

ELY, T.A. and HOWELL, K.C. “Dynamics of Artificial Satellite Orbits with Tesseral Resonances Including the Effects of Luni-Solar Perturbations,”

*International Journal of Dynamics and Stability of Systems*, Vol. 12, No. 4, 1997, pp. 243–269.

MathSciNetMATHCrossRefGoogle Scholar[6]

ELY, T.A. and HOWELL, K.C. “East-West Stationkeeping of Satellite Orbits with Resonant Tesseral Harmonics,”

*Acta Astronautica*, Vol. 46, No. 1, 2000, pp. 1–15.

CrossRefGoogle Scholar[7]

FERREIRA, L.D.D. and VILHENA DE MORAES, R. “GPS Satellites Orbits: Resonance,” *Mathematical Problems in Engineering*, Vol. 2009, Article ID 347835, 12 pp.

[8]

DELEFLIE, F., LEGENDRE, P., EXERTIER, P. and BARLIER, F. “Long Term Evolution of the Galileo Constellation due to Gravitational Forces,”

*Advances in Space Research*, Vol. 36, 2005, pp. 402–411.

CrossRefGoogle Scholar[9]

GARFINKEL, B. “Formal Solution in the Problem of Small Divisors,”

*Astronomical Journal*, Vol. 71, No. 8, 1966, pp. 657–669.

MathSciNetCrossRefGoogle Scholar[10]

BROUWER, D. and CLEMENCE, G.M.

*Methods of Celestial Mechanics*, Academic Press, New York and London, 1961, pp. 296ff.

Google Scholar[11]

BOCCALETTI, D. and PUCACCO, G. *Theory of Orbits. 2: Perturbative and Geometrical Methods*, Springer, A&A library, 1998, p. 10.

[12]

ALLAN, R.R. “Resonance Effects due to the Longitude Dependence of the Gravitational Field of a Rotating Primary,”

*Planetary and Space Science*, Vol. 15, 1967, pp. 53–76.

CrossRefGoogle Scholar[13]

LANE, M.T. “An Analytical Treatment of Resonance Effects on Satellite Orbits,”

*Celestial Mechanics*, Vol. 42, Nos. 1–4, 1988, pp. 3–38.

Google Scholar[14]

SOCHILINA, A.S. “On the Motion of a Satellite in Resonance with Its Rotating Plane,”

*Celestial Mechanics*, Vol. 26, No. 4, 1982, pp. 337–352.

MATHCrossRefGoogle Scholar[15]

GEDEON, G.S. “Tesseral Resonance Effects on Satellite Orbits,”

*Celestial Mechanics*, Vol. 1, No. 2, 1969, pp. 167–189.

MATHCrossRefGoogle Scholar[16]

KAMEL, A., EKMAN, D. and TIBBITTS, R. “East-West Stationkeeping Requirements of Nearly Synchronous Satellites due to Earth Triaxiality and Luni-Solar Effects,”

*Celestial Mechanics*, Vol. 8, No. 1, 1973, pp. 129–148.

CrossRefGoogle Scholar[17]

ELY, T.A. “Eccentricity Impact on East-West Stationkeeping for Global Positioning System Class Orbits,”

*Journal of Guidance, Control and Dynamics*, Vol. 25, No. 2, 2002, pp. 352–357.

CrossRefGoogle Scholar[18]

BOHLIN, K. “Zur Frage der Convergenz der Reihenentwickelungen in der Störungstheorie,”

*Astronomische Nachrichten*, Vol. 121, No. 2, 1889, 17–24.

MATHCrossRefGoogle Scholar[19]

FERRAZ-MELLO, S. *Canonical Perturbation Theories. Degenerate Systems and Resonance*, 2007, Astrophysics and Space Science Library, Vol. 345, Springer.

[20]

ROMANOWICZ, B.A. “On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory,” *SAO Special Report* 365, 1975, 52 pp; Part II, *SAO Special Report* 373, 1976, 30 pp.

[21]

MOORE, P. “A Resonant Problem of Two Degrees of Freedom,”

*Celestial Mechanics*, Vol. 30, No. 1, 1983, pp. 31–47.

MathSciNetMATHCrossRefGoogle Scholar[22]

MOORE, P. “A Problem of Libration with Two Degrees of Freedom,”

*Celestial Mechanics*, Vol. 33, No. 1, 1984, pp. 49–69.

MathSciNetMATHCrossRefGoogle Scholar[23]

VALK, S., LEMAÎTRE, A. and DELEFLIE, F. “Semi-Analytical Theory of Mean Orbital Motion for Geosynchronous Space Debris under Gravitational Influence,”

*Advances in Space Research*, Vol. 43, 2009, pp. 1070–1082.

CrossRefGoogle Scholar[24]

MCCLAIN, W. D. *A Recursively Formulated First-Order Semianalytic Artificial Satellite Theory Based on the Generalized Method of Averaging, Volume 1: The Generalized Method of Averaging Applied to the Artificial Satellite Problem*, Computer Sciences Corporation CSC/TR-77/6010, 1977 (“the blue book”). Also: *A Semianalytic Artificial Satellite Theory. Volume 1. Application of the Generalized Method of Averaging to the Artificial Satellite Problem*, 1992.

[25]

DANIELSON, D.A., NETA, B. and EARLY, L.W. *Semianalytic Satellite Theory (SST): Mathematical Algorithms*, Naval Postgraduate School, NPS Report NPS-MA-94-001, January 1994.

[26]

FONTE, D.J., *Implementing a* 50 × 50 *Gravity Field in an Orbit Determination System*, Master of Science Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, CSDL-T-1169. June 1993.

[27]

SCHUTZ, B.E. and CRAIG, D.E. “GPS Orbit Evolution: 1998–2000,” Proceedings of the *AIAA/AAS Astrodynamics Specialist Conference*, Denver, Colorado, Aug 14–17, 2000.

[28]

INEICHEN, D., BEUTLER, G. and HUGENTOBLER, U. “Sensitivity of GPS and GLONASS Orbits with Respect to Resonant Geopotential Parameters,”

*Journal of Geodesy*, Vol. 77, 2003, pp. 478–486.

CrossRefGoogle Scholar[29]

FROIDEVAL, L. and SCHUTZ, B.E. “Long arc Analysis of GPS Orbits,” Advances in the Astronautical Sciences, Vol. 124, 2006, pp. 653–664.

Google Scholar[30]

HORI, G.-I. “Theory of General Perturbation with Unspecified Canonical Variable,”

*Publications of the Astronomical Society of Japan*, Vol. 18, No. 4, 1966, pp. 287–296.

Google Scholar[31]

DEPRIT, A. 1969 “Canonical Transformations Depending on a Small Parameter,”

*Celestial Mechanics*, Vol. 1, No. 1, pp. 12–30.

MathSciNetMATHCrossRefGoogle Scholar[32]

CAMPBELL, J.A. and JEFFERYS, W.H. “Equivalence of the Perturbation Theories of Hori and Deprit,”

*Celestial Mechanics*, Vol. 2, No. 4, 1970, pp. 467–473.

MATHCrossRefGoogle Scholar[33]

DEPRIT, A. “Delaunay Normalisations,”

*Celestial Mechanics*, Vol. 26, No. 1, 1982, pp. 9–21.

MathSciNetCrossRefGoogle Scholar[34]

SCHUTZ, B.E. “Numerical Studies in the Vicinity of GPS Deep Resonance,” Advances in the Astronautical Sciences, Vol. 105, 2000, pp. 287–302.

Google Scholar[35]

BROUCKE, R. and CEFOLA, P.J. “On the Equinoctial Orbit Elements,”

*Celestial Mechanics*, Vol. 5, No. 3, 1972, pp. 303–310.

MATHCrossRefGoogle Scholar[36]

HINTZ, G.R. “Survey of Orbit Element Sets,”

*Journal of Guidance, Control and Dynamics*, vol. 31, no. 3, 2008, pp. 785–790.

CrossRefGoogle Scholar[37]

DELHAISE, F. and HENRARD, J. “The Problem of Critical Inclination Combined with a Resonance in Mean Motion in Artificial Satellite Theory,”

*Celestial Mechanics and Dynamical Astronomy*, Vol. 55, 1993, pp. 261–153.

MathSciNetCrossRefGoogle Scholar[38]

KOZAI, Y. “Second-Order Solution of Artificial Satellite Theory without Air Drag,”

*Astronomical Journal*, Vol. 67, No. 7, 1962, pp. 446–461.

MathSciNetCrossRefGoogle Scholar[39]

DEPRIT, A. and ROM, A. “The Main Problem of Artificial Satellite Theory for Small and Moderate Eccentricities,”

*Celestial Mechanics*, Vol. 2, No. 2, 1970, pp. 166–206.

MathSciNetMATHCrossRefGoogle Scholar[40]

MÉTRIS, G. *Théorie du mouvement des satellites artificiels — Développement des équations du mouvement moyen — Application à l’étude des longues périodes*, Ph.D. Dissertation, Observatoire de Paris, 1991, 188 p.

[41]

LYDDANE, R.H. “Small Eccentricities or Inclinations in the Brouwer Theory of the Artificial Satellite,”

*Astronomical Journal*, Vol. 68, 1963, pp. 555–558.

MathSciNetCrossRefGoogle Scholar[42]

CHAO, C.-C.G.

*Applied Orbit Perturbation and Maintenance*, The Aerospace Press, El Segundo, California — AIAA Inc., Reston, Virginia, 2005, p. 87.

Google Scholar[43]

LARA, M., SAN-JUAN, J.F. and CEFOLA, P. “Long-Term Evolution of Galileo Operational Orbits by Canonical Perturbation Theory,” presented as paper IAC-C1.3.9 at the, 62nd International Astronautical Congress, Cape Town, South Africa, 2011.

[44]

GARFINKEL, B. “A Theory of Libration,”

*Celestial Mechanics*, Vol. 13, No. 2, 1976, pp. 229–246.

MathSciNetMATHCrossRefGoogle Scholar[45]

KAULA, W.M.

*Theory of Satellite Geodesy*, Blaisdell Publishing Company, Waltham, Massachusetts, 1966, p. 50. Reprinted by Dover Publications, Inc., Mineola, N.Y., 2000.

Google Scholar[46]

SANDERS, J.A. and VERHULST, F.

*Averaging Methods in Nonlinear Dynamical Systems*, Berlin-Heidelberg-New York-Tokyo, Springer-Verlag 1985.

MATHGoogle Scholar[47]

PROULX, R., MCCLAIN, W., EARLY, L. and CEFOLA, P. “A Theory for the Short Periodic Motion due to the Tesseral Harmonic Gravity Field,” presented as paper AAS 81-180 at the AAS/AIAA Astrodynamics Conference, North Lake Tahoe, Nev., August 1981.

[48]

CEFOLA, P. and BROUCKE, R. “On the Formulation of the Gravitational Potential in Terms of Equinoctial Variables,” presented as paper AIAA 75-9 at the AIAA 13th Aerospace Sciences Meeting, Pasadena, CA, January 1975.

[49]

PARDINI, C. and ANSELMO, L. *SATRAP: Satellite Reentry Analysis Program*, Internal Report C94-17, CNUCE/CNR, Pisa, Italy, 30 August 1994.

[50]

CHAO, C.C. and GICK, R.A. “Long-Term Evolution of Navigation Satellite Orbits: GPS/GLONASS/GALILEO,”

*Advances in Space Research*, Vol. 34, 2004, pp. 1221–1226.

CrossRefGoogle Scholar[51]

DELEFLIE, F., ROSSI, A., PORTMANN, C, MÉTRIS, G. and BARLIER, F. “Semi-Analytical Investigations of the Long Term Evolution of the Eccentricity of Galileo and GPS-Like Orbits,”

*Advances in Space Research*, Vol. 47, 2011, pp. 811–821.

CrossRefGoogle Scholar[52]

CARTER, S.S. *Precision Orbit Determination From GPS Receiver Navigation Solutions*, Master of Science Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. CSDL-T-1260, June 1996.

[53]

LARA, M., SAN-JUAN, J.F., FOLCIK, Z.J. and CEFOLA, P. “Deep Resonant GPS-Dynamics due to the Geopotential,” Advances in the Astronautical Sciences, Vol. 140, 2011, pp. 1985–2004.

Google Scholar