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  • 1
    Electronic Resource
    Electronic Resource
    Explicit Symplectic Integrator for Rotating Satellites (2000)
    Springer
    Celestial mechanics and dynamical astronomy 77 (2000), S. 127-137 
    Details
    ISSN: 1572-9478
    Keywords: numerical methods ; symplectic integrators ; satellite rotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An explicit symplectic integrator is constructed for the problem of a rotating planetary satellite on a Keplerian orbit. The spin vector is fixed perpendicularly to the orbital plane. The integrator is constructed according to the Wisdom-Holman approach: the Hamiltonian is separated in two parts so that one of them is multiplied by a small parameter. The parameter depends on the satellite’s shape or the eccentricity of its orbit. The leading part of the Hamiltonian for small eccentricity orbits is similar to the simple pendulum and hence integrable; the perturbation does not depend on angular momentum which implies a trivial ‘kick’ solution. In spite of the necessity to evaluate elliptic function at each step, the explicit symplectic integrator proves to be quite efficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008354823635
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  • 2
    Electronic Resource
    Electronic Resource
    Keplerian expansions in terms of Henrard's practical variables (1994)
    Springer
    Celestial mechanics and dynamical astronomy 58 (1994), S. 237-244 
    Details
    ISSN: 1572-9478
    Keywords: Keplerian expansions ; Henrard variables ; Lie transforms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Formulae for the Keplerian expansions in terms of Henrard's “practical variables” are given. Two different methods were applied: one using the Bessel functions and one based on the Lie transforms. The former involves less series products, but the latter is more flexible and universal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00691976
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  • 3
    Electronic Resource
    Electronic Resource
    Lunisolar Apsidal Resonances at low Satellite Orbits (1999)
    Springer
    Celestial mechanics and dynamical astronomy 74 (1999), S. 253-274 
    Details
    ISSN: 1572-9478
    Keywords: artificial satellites ; lunisolar perturbations ; resonances ; analytical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Eccentricity resonances between the secular motion of an Earth satellite's orbit and the longitudes of the Sun and the Moon are studied within a Hamiltonian framework. The problem is approximated in a traditional manner, with the Earth's potential including only the second zonal harmonic, and a Hill‐type approximation for perturbing bodies. For a family of 10 resonances, stable and unstable points are identified and libration widths are estimated. Numerical values are given for the maximum variation of eccentricity available at each resonance. The respective amplitudes of the perigee heights' librations range from 2 to 750 km. The resonances of the solar origin are generally stronger than their lunar counterparts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008379908163
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  • 4
    Electronic Resource
    Electronic Resource
    The Prograde C7 Resonance for Earth and Mars Satellite Orbits (2000)
    Springer
    Celestial mechanics and dynamical astronomy 77 (2000), S. 201-214 
    Details
    ISSN: 1572-9478
    Keywords: artificial satellites ; lunisolar perturbations ; resonances ; analytical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The resonance C7 is a 1:1 eccentricity (apsidal) resonance between the longitude of a satellite's pericentre and the mean longitude of the Sun. A previous paper by the author (Breiter, 1999) identified it as the strongest of the lunisolar apsidal resonances. After the reduction to a single degree of freedom, the problem is studied qualitatively for the prograde orbits around the Earth and Mars. Pitchfork, saddle-node, and saddle connection bifurcations give rise to a complicated phase flow, which may involve up to nine critical points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011114127046
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  • 5
    Electronic Resource
    Electronic Resource
    Symplectic Mapping for Satellites and Space Debris Including Nongravitational Forces (1998)
    Springer
    Celestial mechanics and dynamical astronomy 71 (1998), S. 79-94 
    Details
    ISSN: 1572-9478
    Keywords: artificial satellites ; space debris ; symplectic integrators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The paper presents an efficient algorithm for the study of satellite and space debris orbits on long time intervals. The averaged equations of motion are integrated by means of the implicit midpoint method. This approach is known as a symplectic mapping technique. The perturbing forces included in the mapping are: the geopotential, the atmospheric drag, lunisolar perturbations and the direct radiation pressure (without shadow effects). The influence of the atmosphere is approximated by simple methods for the estimation of integrals. The described mapping is valid for the wide range of orbits including the resonant and the eccentric ones; it can be helpful in practical and theoretical problems. The lifetime of GPS transfer orbits is discussed as an exemplary application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008356915763
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  • 6
    Electronic Resource
    Electronic Resource
    Explicit Symplectic Integrator for Highly Eccentric Orbits (1998)
    Springer
    Celestial mechanics and dynamical astronomy 71 (1998), S. 229-241 
    Details
    ISSN: 1572-9478
    Keywords: numerical methods ; symplectic integrators ; satellite theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An explicit symplectic integrator is constructed for perturbed elliptic orbits of an arbitrary eccentricity. The perturbation should be Hamiltonian, but it may depend on time explicitly. The main feature of the integrator is the use of KS variables in the ten-dimensional extended phase space. As an example of its application the motion of an Earth satellite under the action of the planet's oblateness and of lunar perturbations is studied. The results confirm the superiority of the method over a classical Wisdom–Holman algorithm in both accuracy and computation time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008369619073
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  • 7
    Electronic Resource
    Electronic Resource
    Tesseral harmonic perturbations in radial transverse and binormal components (1990)
    Springer
    Celestial mechanics and dynamical astronomy 48 (1990), S. 375-385 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The formulae for the perturbations in radial, transverse and binormal components of the Earth artificial satellite motion have been derived. Perturbations due to the tesseral part of the geopotential are considered. The geopotential expressed in terms of the orbital elements has the form proposed by Wnuk (1988). The formulae for the perturbations have been obtained using the Hori (1966) method. They can be effectively applied in calculation of the perturbations in the components including the coefficients of the high order and degree tesseral harmonics. The derived formulae reveal no singularities at zero eccentricity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049391
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  • 8
    Electronic Resource
    Electronic Resource
    Abstracts (1993)
    Springer
    Celestial mechanics and dynamical astronomy 57 (1993), S. 403-404 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692489
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  • 9
    Electronic Resource
    Electronic Resource
    On the numerical transformation of variables in perturbation theory (1996)
    Springer
    Celestial mechanics and dynamical astronomy 65 (1996), S. 345-354 
    Details
    ISSN: 1572-9478
    Keywords: Lie series ; numerical integration ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Once the generating function of a Lie-type transformation is known, canonical variables can be transformed numerically by application of a Runge-Kutta type integration method or any other appropriate numerical integration algorithm. The proposed approach avails itself of the fact, that the transformation is defined by a system of differential equations with a small parameter as the independent variable. The integration of such systems arising in the perturbation theories of Hori and Deprit is discussed. The method allows to compute numerical values of periodic perturbations without deriving explicitly the perturbation series. This saving of an algebraic work is achieved at the expense of multiple evaluations of the generator's derivatives.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049499
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  • 10
    Electronic Resource
    Electronic Resource
    First-order theory of weakly eccentric orbital motion (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 191-206 
    Details
    ISSN: 1572-9478
    Keywords: perturbation theory ; small eccentricities ; artificial satellite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Starting from the analytical theory of perturbed circular motions presented in “Celestial Mechanics” (Bois, 1994), this paper presents an extended resolution valid also for small eccentricity orbits. The solution is of the first order of a small parameter characterizing the magnitude of disturbing forces. The solution has the form of Fourier series with the coefficients given by iterative formation laws. The solution is free from singularities due to small eccentricity or inclination. As an example of numerical application the equatorial artificial satellite orbits are analyzed. For some high satellite orbits with small eccentricity the difference between the numerical integration and the analytical model does not exceed few centimeters per one revolution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00693321
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