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1
Content available remote 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
Content available remote 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
Content available remote 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
Content available remote 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
Content available remote 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
Content available remote 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
Content available remote 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
Content available remote 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.
9
Content available remote Optimal Generalized Coplanar Bi-elliptic Transfer Orbits Part II
Kamel O. M., Soliman A. S.
Mechanics and Mechanical Engineering
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2009
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Vol. 13, nr 2
93-104
EN
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.
10
Content available remote Optimal Generalized Coplanar Bi-Elliptic Transfer Orbit Part I
Kamel O. M., Soliman A. S.
Mechanics and Mechanical Engineering
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2009
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Vol. 13, nr 1
73-78
EN
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.
11
Content available remote Velocity Correction in Generalized Hohmann and Bi-elliptic Impulsive Orbital Maneuvers Using Energy Concepts
Kamel O. M., Soliman A. S.
Mechanics and Mechanical Engineering
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2008
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Vol. 12, nr 1
31-49
EN
We applied small tangential impulses due to motor thrusts at peri-apse and apo-apse perpendicular to major axis of the elliptic orbits. Our aim is to obtain a precise final orbit stemming from an initial orbit. We executed these tangential correctional velocities to all the four feasible configurations. The correctional increments of velocities ΔvA & ΔvB at the points A, B for the Hohmann transfer and at the points A, B, C for the Bi-Elliptic transfer induce the precise final orbit. Throughout the treatment we encounter relationships for both cases of transfer that describe the alteration in major axes and eccentricities due to these motor thrusts supplied by a rocket. The whole theory is a correctional improvement process.
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