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Optimum Impulsive Hohmann Coplanar Elliptic Transfer Using Energy Change Concept Part II

100%

Kamel O. M. , Soliman A. S.

Mechanics and Mechanical Engineering

2009

tom Vol. 13, nr 2

81-92

We present an elementary approach for the optimization of the elliptic coplanar coaxial Hohmann type transfer arising from the first principles. We assign the minimized increments of velocities at peri-apse and apo-apse by equating to zero the gradient of Δv1+ Δv2, then resolving a second degree algebraic equation in the variable x (the ratio of the velocities before and after the initial impulse). We consider the four feasible configurations, and we assign the most economic one. By setting e1 = 0, e2 = 0 for the terminal orbits, we confront the original circular Hohmann transfer case promptly.

Optimum Impulsive Hohmann Coplanar Elliptic Transfer (Aggregation of New Useful Relationships) Part I

100%

Kamel O. M.

Mechanics and Mechanical Engineering

2009

tom Vol. 13, nr 1

63-71

We present an elementary approach for the optimization problem relevant to the elliptic coplanar Hohmann type transfer arising from first principles. We assign the minimized increments sum of velocities at peri-apse and apo-apse by the application of the ordinary calculus optimum condition then resolving a simple second degree algebraic equation in the variable x which is the ratio of the velocities after and before the initial impulse. It is demonstrated that the classical elliptic Hohmann type transfer is the most economic one by this elementary representation. Moreover it is a generalized of the classical Hohmann type circular case transfer.

The change in the hyperbolic orbital elements due to application of a small impulse

86%

Kamel O. M. , Soliman A. S. , Ammar M. K.

Mechanics and Mechanical Engineering

2004

tom Vol. 7, nr 2

107-119

The differential variations in the hyperbolic orbital classical element s due to a small impulse in the direction of the velocity vector are computed. We applied the method of Gauss for secular perturbations using the Lagrangian form of planetary equations.

Optimum impulsive Hohmann coplanar elliptic transfer using energy change concept. Part II

86%

Kamel O. M. , Soliman A. S.

Mechanics and Mechanical Engineering

2010

tom Vol. 14, nr 1

105-117

We present an elementary approach for the optimization of the elliptic coplanar coaxial Hohmann type transfer arising from the first principles. We assign the minimized increments of velocities at peri-apse and apo-apse by equating to zero the gradient of Δv1 + Δv2, then resolving a second degree algebraic equation in the variable x (the ratio of the velocities before and after the initial impulse). We consider the four feasible configurations, and we assign the most economic one. By setting e1 = 0, e2 = 0 for the terminal orbits, we confront the original circular Hohmann transfer case promptly.

Optimal Generalized Coplanar Bi-elliptic Transfer Orbits Part II

86%

Kamel O. M. , Soliman A. S.

Mechanics and Mechanical Engineering

2009

tom 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

86%

Kamel O. M. , Soliman A. S.

Mechanics and Mechanical Engineering

2009

tom 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.

Optimum bi-impulsive non coplanar elliptic Hohmann type transfer

58%

Kamel O. M. , Soliman A. S.

Mechanics and Mechanical Engineering

2010

tom Vol. 14, nr 1

81-104

We optimize the Hohmann type bi-impulsive transfer between inclined elliptic orbits having a common center of attraction, for the four feasible configurations. Our criterion for optimization is the characteristic velocity ΔvT = Δv1 + Δv2 which is a measure of fuel consumption. We assigned the optimum value of our variable x (ratio between velocity after initial impulse and velocity before initial impulse) by a numerical solution of an algebraic eight degree equation. We have a single plane change angle α. We present terse new formulae constituting a new alternative approach for tackling the problem. The derivations of formulae of our treatment are simple, straightforward and exceptionally clear. This is advantageous. By this semi-analytic analysis we avoid many complexities and ambiguity that appear in previous work.