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Solution of the Gaussian transfer orbit equations of motion

Kamel O. M., Ammar M. K.

Mechanics and Mechanical Engineering

2011

Vol. 15, nr 1

39-46

This article deals with an orbit transfer problem by the application of only one motor thrust engine impulse at any point (r , v) on the elliptic initial orbit. The terminal orbits are elliptic. We consider the coplanar non-limited duration case. We succeeded to attain an analytical solution for the transfer Lagrange-Gauss modulated equations of motion. We selected the eccentric anomaly to be the independent parameter. We evaluated the integrals that appear in the R.H.S. of the equations of motion for da/dE, de/dE and edw/dE. Accordingly the three elements defining the final orbit are determined from (a - ao), (e - eo), e(w - wo).

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 bi-impulsive non coplanar elliptic Hohmann type transfer

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2010

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.

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

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

Mechanics and Mechanical Engineering

2004

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.