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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Two applications of von Zeipel's method to the stellar three-body problem eliminate the short period terms and establish two new integrals of the motion beyond the classical integrals. The remaining time averaged problem with only the second order Hamiltonian has one additional integral and can be solved. The motion with the third order averaged Hamiltonian included is more complex, in that there may be additional resonances, and the additional integral does not exist in all cases.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An error analysis of resonant orbits for geodesy indicates that attempts to use resonance to recover high order geopotential coefficients may be seriously hampered by errors in the geopotential. This effect, plus the very high correlations (up to .99) of the resonant coefficients with each other and the orbital period in single satellite solutions, makesindividual resonant orbits of limited value for geodesy. Multiple-satellite, single-plane solutions are only a slight improvement over the single satellite case. Accurate determination of high order coefficients from low altitude resonant satellites requires multiple orbit planes and small drift-periods to reduce correlations and effects of errors of non-resonant geopotential terms. Also, the effects of gravity model errors on low-altitude resonant satellites make the use of tracking arcs exceeding two to three weeks of doubtful validity. Because high-altitude resonant orbits are less affected by non-resonant terms in the geopotential, much longer tracking arcs can be used for them.
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  • 5
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In an axially symmetric three-dimensional Riemann-spaceg ik(u 1,u 2)−u 3 represents the cyclic parameter-, a gravitational potential ϕ(u 1,u 2) is given. For all masspoints with equal total energy and equal angular momentum there exists a function Ψ(u 1,u 2) by means of which the equations of motion can be reduced to a simple ordinary second-order differential equation. The function ϕ can be interpreted as the velocity with which the masspoint moves in the two-dimensional spaceu 1,u 2. Of particular interest is the case where the spaceu 1,u 2,u 3 is Euclidean. Ifu 1,u 2 are Cartesian coordinates in a planeu 3=const., and if the tangent vector of the trajectoryu 1(t)u 2(t) has the components cosω, sinω it is shown that the triple integral $$\smallint \smallint \smallint \psi du^1 du^2 d\omega $$ is an invariant integral in Cartan's sense, in other words, if the integral is extended over a domain in a meridian plane at timet=0, it keeps its value at any time.
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  • 7
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits.
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  • 8
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper considers the ground trace of an artificial earth satellite. It determines the effects of the trace caused by perturbations due to atmospheric drag, the oblateness of the earth, and the moon and the sun as a third body. The necessary mathematical relations giving these perturbations which are available in literature are utilized (Betz, 1967; Brouwer and Clemence, 1961; Brouwer and Hori, 1961; Danby, 1962; Escobal, 1965; Kentet al., 1963; Kozai, 1962). Those relations unavailable elsewhere are derived. The computation was done by programming in FORTRAN language and utilizing an IBM 360/65.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An investigation has been made on computing orbits with Picard's method of successive approximations. The perturbations are integrated in the form of a general displacement from a fixed Keplerian reference orbit. Several variation-of-parameters methods are obtained for the integration of the displacement equation. These variation-of-parameters methods could be used as special perturbation or general perturbation methods. The present paper investigates the applications as iterative numerical perturbation techniques. Four different formulations are proposed. They have been implemented on a computer with Chebychev series and their respective advantages and disadvantages are analyzed. Connections with other known perturbation methods are also described.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Peano-Baker method is applied to the integration of the variational equations to produce the partial derivatives used in satellite navigation. In this method the analytic form of the state transition partial derivatives can be factored so that numerical integration is applied only to the departures from a simplified analytical model. The advantage of using the Peano-Baker approach rather than direct integration of the variational equations is that with the Peano-Baker method numerical integration can be performed adequately with low order formulae and relatively large step sizes. Numerical results are indicated.
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