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

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2010

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.

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

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2009

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

Kamel O. M.

Mechanics and Mechanical Engineering

2009

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.