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1
Content available remote A Note on the Generalized Hohmann Transfer Time
100%
Kamel O. M.
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2014
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tom Vol. 18, nr 1
33--35
EN
We calculate the transfer time from the inner to the outer elliptic planetary orbits of a space vehicle for the four feasible configurations and for the circular case. We find that the least time of transfer tT corresponds to the second configuration.
2
Content available remote A Semi - Analytic First Order Jupiter - Saturn Planetary Theory Part I : Outline
100%
Kamel O. M.
|
|
tom Vol. 19, nr 1
17--22
EN
Herein we lay the broad lines for the construction of a first order w.r.t planetary masses Jupiter-Saturn theory - giving the orbital elements of the two planets at any epoch. This is implemented by the evaluation of the R. H. S. of the original first order Hamiltonian equations of motion. The first order Hamiltonian is composed of the first order secular terms and the first order periodic terms. We restrict the periodic terms to be the commensurate ones for the J-S (Jupiter-Saturn) subsystem. We give throughout the text an idea to the extension of the theory to the case of the four major outer planets J-S-U-N.
3
Content available remote Optimum Impulsive Hohmann Coplanar Elliptic Transfer (Aggregation of New Useful Relationships) Part I
100%
Kamel O. M.
Mechanics and Mechanical Engineering
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2009
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tom Vol. 13, nr 1
63-71
EN
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.
4
Content available remote On the Expansion of the Direct Part of the Disturbing Planetary Function
63%
Kamel O. M. , Soliman A. S.
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2016
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tom Vol. 20, nr 4
371--375
EN
We generalize the expansion of Murray–Dermott for the direct part of the disturbing function using Taylor‘s theorem. We present the values of Δ-s for s = 1, 3, 5, . . . which is essential for high order planetary theories. Murray – Dermott executed the expansion for s = 1 which is necessary for only first order theories.
5
Content available remote A second order secular J-S planetary theory. Part I, Lemma
63%
Kamel O. M. , Soliman A. S.
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2018
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tom Vol. 22, nr 4
871--874
EN
A concise lemma is given for the construction of a semi-analytic Hamiltonian second order secular J-S planetary theory using the Jacobi-Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.
6
Content available remote Optimum impulsive Hohmann coplanar elliptic transfer using energy change concept. Part II
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
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2010
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tom Vol. 14, nr 1
105-117
EN
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.
7
Content available remote Optimum bi-impulsive non coplanar elliptic Hohmann type transfer
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
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2010
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tom 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.
8
Content available remote Velocity Correction in Generalized Hohmann and Bi-elliptic Impulsive Orbital Maneuvers Using Energy Concepts
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
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2008
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tom 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.
9
Content available remote A Semi-Analytic First Order Jupiter-Saturn Planetary Theory. Part II
63%
Kamel O. M. , Soliman A. S.
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2016
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tom Vol. 20, nr 3
233--247
EN
In this part we present the algebraic calculus computations related to the Hamiltonian equations of motion for the Jupiter – Saturn subsystem. Also we give a comment on the methods of the solution for the system of linear and nonlinear differential equations describing the motion of this subsystem.
10
Content available remote A Semi - Analytic First Order Jupiter - Saturn Planetary Theory. Part II
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
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2015
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tom Vol. 19, nr 2
103--118
EN
In this part we present the algebraic calculus computations related to the Hamiltonian equations of motion for the Jupiter – Saturn subsystem. Also we give a comment on the methods of the solution for the system of linear and nonlinear differential equations describing the motion of this subsystem.
11
Content available remote Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part II
63%
Kamel O. M. , Soliman A. S.
|
|
tom Vol. 16, nr 2
81--89
EN
We express the geometrical and algebraic aspects of the problem of galactic rotation on the motion of the stars represented by fig. (2). We verify the equations involving third order terms of the orbits of the stars. That means taking into account higher order terms in our analysis, namely up to O(r=R0)3. These terms allow a generalization and high precision for the results. We acquired a higher order Taylor’s expansion for V as denoted in fig. (2). U′, V ′ are the linear components of the velocity of the group of stars S. After some lengthy expansions and reductions, we obtained the formulae for U′, V ′. Consequently ξ, ƞ, Ϛ the linear components of S corresponding to the two proper motion equalities in galactic longitude and latitude and radial velocity Δρ. Expansions are performed up to the third order in (r=R0).
12
Content available remote Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part II
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
|
2013
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tom Vol. 17, nr 3
261--268
EN
We express the geometrical and algebraic aspects of the problem of galactic rotation on the motion of the stars represented by fig. (2). We verify the equations involving third order terms of the orbits of the stars. That means taking into account higher order terms in our analysis, namely up to O(r/R0)3. These terms allow a generalization and high precision for the results. We acquired a higher order Taylor’s expansion for V as denoted in fig. (2). U‘, V‘ are the linear components of the velocity of the group of stars S. After some lengthy expansions and reductions, we obtained the formulae for U‘, V‘. Consequently [...], η, ζ the linear components of S corresponding to the two proper motion equalities in galactic longitude and latitude and radial velocity Δρ. Expansions are performed up to the third order in (r/R0).
13
Content available remote Optimum Impulsive Hohmann Coplanar Elliptic Transfer Using Energy Change Concept Part II
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
|
2009
|
tom Vol. 13, nr 2
81-92
EN
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.
14
Content available remote Optimal Generalized Coplanar Bi-elliptic Transfer Orbits Part II
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
|
2009
|
tom 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.
15
Content available remote Optimal Generalized Coplanar Bi-Elliptic Transfer Orbit Part I
63%
Kamel O. M. , Soliman A. S.
Mechanics and Mechanical Engineering
|
2009
|
tom 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.
16
Content available remote Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part I
51%
Kamel O. M. , Soliman A. S. , Ammar M. K.
Mechanics and Mechanical Engineering
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2012
|
tom Vol. 16, nr 1
41--49
EN
We expand Δρ the radial velocity of a group of stars moving around the center of galaxy, firstly in circular orbits. The expansion of Δρ is performed up to the third order of O(r=R0)3. A new result is encountered. The Oort constant is splitted into 3 parts A1, A2, A3 instead of one constant A. Moreover we verify the problem when the motion of the stars is elliptic. For proper motion components, there is no split of the second Oort‘s constant B. In all involved expansions orders of magnitude higher than the third in ΔR or r=R0 are neglected.
17
Content available remote The change in the hyperbolic orbital elements due to application of a small impulse
51%
Kamel O. M. , Soliman A. S. , Ammar M. K.
Mechanics and Mechanical Engineering
|
2004
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tom Vol. 7, nr 2
107-119
EN
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.
18
Content available remote The expansion of the inverse of the mutual distance between two planets raised to any real integer using Taylor theorem and elliptic expansions Part I, Theoretical results
51%
Elmabsout B. , Kamel O. M. , Soliman A. S.
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2018
|
tom Vol. 22, nr 4
1175--1195
EN
We introduce in this part the method to obtain the literal expansion of the mutual distance between two planets of the solar system raised to any negative real integer.
19
Content available remote Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part I
51%
Kamel O. M. , Soliman A. S. , Ammar M. K.
Mechanics and Mechanical Engineering
|
2013
|
tom Vol. 17, nr 3
251--259
EN
We expand Δfi the radial velocity of a group of stars moving around the center of galaxy, firstly in circular orbits. The expansion of Δfi is performed up to the third order of O(r/R0)3. A new result is encountered. The Oort constant is splitted into 3 parts A1, A2, A3 instead of one constant A. Moreover we verify the problem when the motion of the stars is elliptic. For proper motion components, there is no split of the second Oort‘s constant B. In all involved expansions orders of magnitude higher than the third in ΔR or r/R0 are neglected.
20
Content available remote A First Order Jupiter Saturn Planetary Theory. Numerical Results
51%
Kamel O. M. , Soliman A. S. , El Mabsout B.
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2016
|
tom Vol. 20, nr 1
59--73
EN
We present the numerical analysis solution of the eight ordinary non linear differential equations of a first order secular J – S planetary theory. There is no general solution for these equations. We deal with the Poincare’ variables Hu, Ku, Pu, Qu; u=1,2 only. The solution is approximative, since we confine our treatment to a first order secular theory and truncate the Poisson series expansions at the fourth power in eccentricity – inclination.
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