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1

Self-maintenance orbits using the perturbations due to air drag and due to Earth’s oblateness

Amin Mohamed R.

Mechanics and Mechanical Engineering

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2020

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Vol. 24, nr 1

56--60

EN

The focus of this paper is the design of a selfmaintenance orbit using two natural forces against each other. The effect of perturbations due to Earth’s oblateness up to the third order on both the semi-major axis and eccentricity for a low Earth orbit satellite together with the perturbation due to air drag on the same orbital parameters were used, in order to create self-maintenance orbits. Numerical results were simulated for a low earth orbit satellite,which substantiates the applicability of the results.

2

Optimal generalized Hohmann transfer with plane change using lagrange multipliers

Kamel O. M., Soliman A. S., Amin M. R.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 1

11--16

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.

3

The optimality of the impulsive Hohmann coplanar elliptic transfer using energy change concepts aggregation of new useful relationships. Part II

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 1

47-60

EN

In this part we investigate all the four feasible configurations for the generalized Hohmann type transfer. We assign the minimized characteristic velocity (Δv1+Δv2)Min by the application of ordinary infinitesimal calculus optimum conditions. By some algebraic manipulations, we determine the independent variables (x)Min. In addition, we considered the analysis relevant to the two parameters x, y relevant to the two impulses at points A, B. It is demonstrated that the elliptic Hohmann type transfer is the most economic one by this new representation.

4

Solution of the Gaussian transfer orbit equations of motion

Kamel O. M., Ammar M. K.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 1

39-46

EN

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).

5

On the hyperbolic fly past problem as a velocity amplifier using the elliptic Hohmann transfer

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

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 1

25-38

EN

We investigate the problem of fly past of a space vehicle traveling in a generalized elliptic Hohmann transfer system between the elliptic orbits of the Earth and Jupiter around the Sun. We consider the four feasible elliptic Hohmann configurations. We begin our treatment by a more precise expression for the hyperbolic excess velocity, because we deal with the elliptic not the circular Hohmann case. We assign the semi-major axes and the eccentricity of the hyperbolic trajectory that lies within the sphere of influence of the Jovian planet. Whence we have a more accurate determination of the elements of the hyperbolic trajectory before the vehicle's departure out of Jupiter's influence sphere to follow its trip to a further outer planet of the local solar system.

6

On the generalized Hohmann transfer with plane change using energy concepts. Part I

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 2

183-191

EN

We investigate in this article 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. 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 assume the elements of the two impulse Hohmann generalized configuration (the case of elliptic, non coplanar orbits) to be a1, e1, a2, e2, aT, eT. From the very beginning, we should assign θ = α 1 + α 2, the total plane change required. α 1 is the plane change at the first instantaneous impulse at peri-apse, which will be minimized, and α 2 the plane change at the second instantaneous thrust at apo-apse.

7

Determination of the classical orbital elements of the perturbed and perturbing planets from first principles. Part I: Outline

Kamel O. M.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 2

193-195

EN

In this outline we present a rather simple method to solve the planetary perturbation problem. We do not avoid the introduction of the expansion of the planetary disturbing function, the formulae of the elliptic expansions and the truncation of the Poisson series at the desired degree. We should remark that all orders of magnitude of the masses of the planets are taken into consideration, which is a very important result of this approach which we encounter in the order by order approach of planetary theory.

8

Optimum bi-impulsive non coplanar elliptic Hohmann type transfer

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

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2010

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Vol. 14, nr 1

81-104

EN

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.