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2 Mechanics and Mechanical Engineering

2 2009

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Optimal Generalized Coplanar Bi-elliptic Transfer Orbits Part II

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2009

Vol. 13, nr 2

93-104

In this part II, we extend our analysis to include all of the four feasible configurations. We have four generalized bi-elliptic configurations for the transfer problem, for a central gravitational field. We apply three impulses as usual for the bi-elliptic case, at the points A, C, B. x, z are our independent variables and are equal to the ratio between values of the velocities after and before the application of the impulses at points of pericenter and apocenter. Similarly y is defined as the corresponding parameter for the point C. We utilize the optimum condition of ordinary infinitesimal calculus for algebraic functions to evaluate the minimum values of x, z, y. In this part II we expand the domain of application of the numerical results.

Optimal Generalized Coplanar Bi-Elliptic Transfer Orbit Part I

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2009

Vol. 13, nr 1

73-78

We have four feasible simple Bi-elliptic configurations for the transfer problem, for a central gravitational field. We restrict our selves to the first one in this part. We apply three impulses at the points A, C, B. x, z are our independent variables and are equal to the ratio between values of the velocities after and before the application of the impulses at points A, B respectively. Similarly y is defined as the corresponding parameter for the point C. We utilize the optimum condition of ordinary calculus for algebraic functions, to evaluate minimum values of x, z, y. We adopt the Earth - Mars bi-elliptic coplanar transfer system as an example, for the first configuration, to evaluate the numerical minimum values of x, z, y. In part II, we shall consider the other three configurations and expand to domain of application of the numerical results.