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Optimal generalized Hohmann transfer with plane change using lagrange multipliers

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The optimized orbit transfer of a space vehicle, revolving initially around the primary, in a similar orbit to that of the Earth around the Sun, in an elliptic trajectory, to another similar elliptic orbit of an adequate outer planet is studied in this paper. We assume the elements of the initial orbit to be that of the Earth, and the elements of the final orbit to be that of an outer adequate planet, Mars for instance. We consider the case of two impulse generalized Hohmann non coplanar orbits. We need noncoplanar (plane change) maneuvers mainly because: 1) a launch-site location restricts the initial orbit inclination for the vehicle; 2) the direction of the launch can influence the amount of velocity the booster must supply, so certain orientations may be more desirable; and 3) timing constraints may dictate a launch window that isn’t the best, from which we must make changes[3]. We used the Lagrange multipliers method to get the optimum of the total minimum energy required ΔVT , by optimizing the two plane change angles 1 and 2, where 1 is the plane change at the first instantaneous impulse at peri-apse, and 2 the plane change at the second instantaneous thrust at apo-apse. We adopt the case of Earth - Mars, as a numerical example.
Rocznik
Strony
11--16
Opis fizyczny
Bibliogr. 9 poz., rys.
Twórcy
autor
  • Astronomy and Space Science Dept., Faculty of Sciences, Cairo University, Giza, Egypt
  • Theoretical Physics Dept., National Research Center, Dokki, Giza, Egypt
autor
  • Theoretical Physics Dept., National Research Center, Dokki, Giza, Egypt
Bibliografia
  • [1] Prussing, J. E. and Conway, B. A.: Orbital Mechanics, Oxford University Press, 1993.
  • [2] Ehricke, K. A.: Space Flight, Dynamics, Van Nostrand, Vol. 2, 1962.
  • [3] Vallado, D. A.: Fundamentals of Astrodynamics and Applications, 3rd edition, Springer, 2007.
  • [4] Lawden, D. F.: Optimal Transfers Between Coplanar Elliptical Orbits, J. Guidance, Engineering notes, 15, 3, 1991.
  • [5] Kamel, O. M. and Soliman, A. S.: On transfer between elliptical coplanar coaxial orbits, Bulletin of the Faculty of Sciences, Cairo University, 67, 1999.
  • [6] Kamel, O. M. and Soliman, A. S.: On the generalized Hohmann transfer with plane change using energy concepts, Part I, Mechanics and Mechanical Engineering, 15, 2, 183-191, 2011.
  • [7] Chobotov, V. A.: Orbital Mechanics, 3rd edition, AIAA, Education Series, 2002.
  • [8] Bertsekas, D. P.: Constrained Optimization and Lagrange Multiplier Methods Academic Press, 1 st ed., 1982.
  • [9] Murray, C. D. and Dermott, S. F.: Solar System Dynamics, Cambridge University Press, 1999.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-abccd6cb-7548-4d69-929e-a0a63001cdb4
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