Complete list of academic references used in the Apogee documentation.

Textbooks¶

Orbital Mechanics¶

Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics (Revised Edition). AIAA Education Series. ISBN: 978-1563473425

Curtis, H.D. (2013). Orbital Mechanics for Engineering Students (3rd Edition). Butterworth-Heinemann. ISBN: 978-0080977478

Vallado, D.A. (2013). Fundamentals of Astrodynamics and Applications (4th Edition). Microcosm Press. ISBN: 978-1881883180

Rocket Propulsion¶

Sutton, G.P. & Biblarz, O. (2016). Rocket Propulsion Elements (9th Edition). Wiley. ISBN: 978-1118753651

Numerical Methods¶

Stoer, J. & Bulirsch, R. (2002). Introduction to Numerical Analysis (3rd Edition). Springer. ISBN: 978-0387954523

Nocedal, J. & Wright, S. (2006). Numerical Optimization (2nd Edition). Springer. ISBN: 978-0387303031

Hairer, E., Nørsett, S.P., & Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems (2nd Edition). Springer. ISBN: 978-3540566700

Ascher, U.M. & Petzold, L.R. (1998). Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM. ISBN: 978-0898714128

Papers¶

Runge-Kutta Methods¶

Tsitouras, Ch. (2011). "Runge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption." Computers & Mathematics with Applications, 62(2), 770-775. DOI: 10.1016/j.camwa.2011.06.002

Levenberg-Marquardt¶

Moré, J.J. (1978). "The Levenberg-Marquardt Algorithm: Implementation and Theory." Lecture Notes in Mathematics, 630, 105-116. DOI: 10.1007/BFb0067700

Levenberg, K. (1944). "A method for the solution of certain non-linear problems in least squares." Quarterly of Applied Mathematics, 2(2), 164-168.

Marquardt, D.W. (1963). "An algorithm for least-squares estimation of nonlinear parameters." Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441.

Quasi-Newton Methods¶

Broyden, C.G. (1965). "A class of methods for solving nonlinear simultaneous equations." Mathematics of Computation, 19(92), 577-593. DOI: 10.1090/S0025-5718-1965-0198670-6

Dennis, J.E. & Moré, J.J. (1974). "A characterization of superlinear convergence and its application to quasi-Newton methods." Mathematics of Computation, 28(126), 549-560.

Technical Reports¶

NOAA/NASA/USAF (1976). U.S. Standard Atmosphere, 1976. U.S. Government Printing Office. NOAA-S/T 76-1562.

Software Documentation¶

Diffrax: https://docs.kidger.site/diffrax/

JAX: https://jax.readthedocs.io/

ussa1976: https://pypi.org/project/ussa1976/

BibTeX Entries¶

@book{battin1999,
  author    = {Richard H. Battin},
  title     = {An Introduction to the Mathematics and Methods of Astrodynamics},
  publisher = {AIAA Education Series},
  year      = {1999},
  edition   = {Revised}
}

@book{curtis2013,
  author    = {Howard D. Curtis},
  title     = {Orbital Mechanics for Engineering Students},
  publisher = {Butterworth-Heinemann},
  year      = {2013},
  edition   = {3rd}
}

@article{tsitouras2011,
  author  = {Ch. Tsitouras},
  title   = {Runge-Kutta pairs of order 5(4)},
  journal = {Computers \& Mathematics with Applications},
  volume  = {62},
  pages   = {770--775},
  year    = {2011}
}

@article{more1978,
  author  = {Jorge J. Moré},
  title   = {The Levenberg-Marquardt Algorithm},
  journal = {Lecture Notes in Mathematics},
  volume  = {630},
  pages   = {105--116},
  year    = {1978}
}

@article{broyden1965,
  author  = {C. G. Broyden},
  title   = {A class of methods for solving nonlinear equations},
  journal = {Mathematics of Computation},
  volume  = {19},
  pages   = {577--593},
  year    = {1965}
}