Optimal generalized Hohmann transfer with plane change using lagrange multipliers

• Autorzy: Kamel, O. M. , Soliman, A. S. , Amin, M. R.
• 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.

Słowa kluczowe

PL

mechanika orbitalna; eliptyczny transfer Hohmanna; problem optymalizacyjny; mnożniki Lagrange'a

EN

orbital mechanics; elliptic Hohmann transfer with plane change; optimization problem; Lagrange multipliers

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. 21, nr 1
• Strony: 11--16
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Kamel, O. M.

• Astronomy and Space Science Dept., Faculty of Sciences, Cairo University, Giza, Egypt,

autor

Soliman, A. S.

• Theoretical Physics Dept., National Research Center, Dokki, Giza, Egypt,

autor

Amin, M. R.

• 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).