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  • 1980-1984  (1)
  • 1970-1974  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Regularization and the computation of optimal trajectories (1970)
    Springer
    Celestial mechanics and dynamical astronomy 2 (1970), S. 319-333 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A completely regular form for the differential equations governing the three-dimensional motion of a continuously thrusting space vehicle is obtained by using the Kustaanheimo-Stiefel regularization. The differential equations for the thrusting rocket are transformed using the K-S transformation and an optimal trajectory problem is posed in the transformed space. The canonical equations for the optimal motion in the transformed space are regularized by a suitable change of the independent variable. The transformed equations are regular in the sense that the differential equations do not possess terms with zero divisors when the motion encounters a gravitational force center. The resulting equations possess symmetry in form and the coefficients of the dependent variables are slowly varying quantities for a low-thrust space vehicle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01235125
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Equivalence of the generalized Lie-Hori method and the method of averaging (1984)
    Springer
    Celestial mechanics and dynamical astronomy 33 (1984), S. 1-20 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01231091
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    Paper (German National Licenses)
    Fulltext
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