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All issues Volume 10 / No 3 (2015) Math. Model. Nat. Phenom., 10 3 (2015) 91-104 References
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Issue
Math. Model. Nat. Phenom.
Volume 10, Number 3, 2015
Model Reduction
Page(s) 91 - 104
DOI https://doi.org/10.1051/mmnp/201510308
Published online 22 June 2015
  1. A. Adrover, F. Creta, M. Giona, M. Valorani, V. Vitacolonna. Natural Tangent Dynamics with Recurrent Biorthonormalization: A Geometric Computational Approach to Dynamical Systems Exhibiting Slow Manifolds and Periodic/Chaotic Limit Sets. Physica D, (2) 213 (2006), 121–146. [CrossRef] [Google Scholar]
  2. E.M. Alessi, G. Gómez, J.J. Masdemont. Leaving The Moon by Means of Invariant Manifolds of Libration Point Orbits, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009), 4153–4167. [CrossRef] [Google Scholar]
  3. L. Barreira, Y.B. Pesin. Lyapunov Exponents and Smooth Ergodic Theory. University Lecture Series 23. American Mathematical Society, Providence, 2002. [Google Scholar]
  4. M. Belló, G. Gómez, J.J. Masdemont. Invariant Manifolds, Lagrangian Trajectories and Space Mission Design. In: Space Manifold Dynamics. Springer, 2010, 1–96. [Google Scholar]
  5. M. Branicki, A. M. Macho, S. Wiggins. A Lagrangian Description of Transport Associated with a Front-Eddy Interaction: Application to Data from the North-Western Mediterranean Sea. Physica D, 240 (2011), 282–304. [CrossRef] [Google Scholar]
  6. E. Chiavazzo, A.N. Gorban, I.V. Karlin. Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics. Comm. in Comp. Physics, 2 (5) (2007), 964–992. [Google Scholar]
  7. L. Dieci, E.S. Van Vleck. Lyapunov Spectral Intervals: Theory and Computation. SIAM J. Numerical Analysis, 40 (2) (2002), 516–542. [CrossRef] [Google Scholar]
  8. E.J. Doedel, V.A. Romanov, R.C. Paffenroth, H.B. Keller, D.J. Dichmann, J. Galán-Vioque, A. Vanderbauwhede. Elemental Periodic Orbits associated with the Libration Points in the Circular Restricted 3-Body Problem. International Journal of Bifurcation and Chaos, 17 (8) (2007), 2625–2677. [CrossRef] [Google Scholar]
  9. E.J. Doedel, AUTO, ftp://ftp.cs.concordia.ca/pub/doedel/auto. [Google Scholar]
  10. D.C. Folta, T.A. Pavlak, A.F. Haapala, K.C. Howell, M.A. Woodard. Earth-Moon Libration Point Stationkeeping: Theory, Modeling, and Operations. Acta Astronautica, 94 (1) (2014), 421–433. [CrossRef] [Google Scholar]
  11. C. Froeschle, E. Lega, R. Gonczi. Fast Lyapunov Indicators: Application to Asteroidal Motion. Celestial Mechanics and Dynamical Astronomy, 67 (1997), 41–62. [CrossRef] [MathSciNet] [Google Scholar]
  12. C.W. Gear, T.J. Kaper, I.G. Kevrekidis, A. Zagaris. Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes. SIAM J. Appl. Dyn. Syst., 4 (2005), 711–732. [CrossRef] [MathSciNet] [Google Scholar]
  13. G.H. Golub, C.F. Van Loan. Matrix Computations, 3rd Edition. The Johns Hopkins University Press, Baltimore, 1996. [Google Scholar]
  14. G. Gómez, J. Llibre, R. Martínez, C. Simó. Station Keeping of Libration Point Orbits. Technical Report ESOC Contract 5648/83/D/JS(SC), 1985. [Google Scholar]
  15. G. Gómez, J. Masdemont, C. Simó. Study of the Transfer from the Earth to a Halo Orbit Around the Equilibrium Point L1. Celestial Mechanics and Dynamical Astronomy, 56 (1993), 541–562. [Google Scholar]
  16. G. Haller. Finding Finite-Time Invariant Manifolds in Two-Dimensional Velocity Fields. Chaos, 10 (1) (2000), 99–108. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. B. Hasselblatt, Y.B. Pesin. Partially Hyperbolic Dynamical Systems. In: B. Haselblatt and A. Katok (Eds.), Handbook of Dynamical Systems. vol. 1B. Elsevier, New York, 2005. [Google Scholar]
  18. K.C. Howell, B. Barden, M. Lo. Application of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission. Journal of Astronautics Science, 45 (2) (1997), 161–178. [Google Scholar]
  19. T.M. Keeter. Station-Keeping Strategies for Libration Point Orbits: Target Point and Floquet Mode Approaches. Ph.D. Dissertation. Purdue University, 1994. [Google Scholar]
  20. W.S. Koon, M.W. Lo, J.E. Marsden, S.D. Ross. Heteroclinic Connections between Periodic Orbits and Resonance Transitions in Celestial Mechanics. Chaos, 10 (2) (2000), 427-469. [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. S.H. Lam, D.A. Goussis. The CSP Method for Simplifying Kinetics. Int. J. Chemical Kinetics, 26 (1994), 461–486. [Google Scholar]
  22. U. Maas, S.B. Pope. Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space. Combustion and Flame, 88 (1992), 239–264. [Google Scholar]
  23. K.D. Mease. Multiple Timescales in Nonlinear Flight Mechanics: Diagnosis and Modeling. Applied Mathematics and Computation, 164 (2005), 627–648. [CrossRef] [Google Scholar]
  24. K.D. Mease, U. Topcu, E. Aykutluğ, M. Maggia. Characterizing Two-Timescale Nonlinear Dynamics Using Finite-Time Lyapunov Exponents and Vectors. (2014). arXiv:0807.0239v3 [math.DS]. [Google Scholar]
  25. D.S. Naidu, A.J. Calise. Singular Perturbations and Timescales in Guidance and Control of Aerospace Systems: a Survey,. J. Guidance, Control and Dynamics, 24 (6) (2001), 1057–1078. [CrossRef] [Google Scholar]
  26. R.E. O’Malley. Singular Perturbation Methods for Ordinary Differential Equations. Springer-Verlag, New York, 1991. [Google Scholar]
  27. M.R. Roussel, S.J. Fraser. Geometry of the Steady-State Approximation: Perturbation and Accelerated Convergence Methods. J. Chem. Phys., 93 (3) (1990), 1072–1081. [CrossRef] [Google Scholar]
  28. L.A. Segel, M. Slemrod. The Quasi-Steady-State Assumption: a Case Study in Perturbation. SIAM Review, 31 (3) (1989), 446–477. [Google Scholar]
  29. S. C. Shadden, F. Lekien, J. E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows. Physica D, 212 (2005), 271–304. [NASA ADS] [CrossRef] [Google Scholar]
  30. C.R. Short, K.C. Howell. Flow Control Segment and Lagrangian Coherent Structure Approaches for Application in Multi-Body Problems. Acta Astronautica 94 (2014), 562–607. [CrossRef] [Google Scholar]
  31. C. Simó, G. Gómez, J. Llibre, R. Martínez. Station Keeping of a Quasiperiodic Halo Orbit Using Invariant Manifolds. In: Proceedings of the Second International Symposium on Spacecraft Flight Dynamics. Darmstadt, FR Germany, 20-23 October, 1986 (ESA SP-255, Dec. 1986). [Google Scholar]
  32. V. Szebehely. Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York, 1967. [Google Scholar]
  33. H. Wan, B.F. Villac. Lunar L1 Earth-Moon Propellant Depot Orbital and Transfer Options Analysis. AAS 13-885, (2013). [Google Scholar]
  34. H. Wan, personal communication, 2013. [Google Scholar]
  35. S. Yoden, M. Nomura. Finite-Time Lyapunov Stability Analysis and Its Application to Atmospheric Predictability. J. Atmospheric Sciences, 50 (11) (1993), 1531–1543. [CrossRef] [Google Scholar]

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