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  • 1
    Electronic Resource
    Electronic Resource
    The two-body problem with radiation pressure in a rotating reference frame (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 287-313 
    Details
    ISSN: 1572-9478
    Keywords: Two-body problem ; radiation pressure ; horseshoes ; chaos ; three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study a perturbed Newtonian two-body problem, in which the perturbation is due to a force field of constant magnitude but rotating direction. By considering this system as a perturbation of the non-rotating case a Melnikov-type analysis allows us to show the existence of horseshoes in the level sets of the Hamiltonian and the subsequent sensitive dependence on initial conditions and non-integrability. We discuss the consequences of these results for a particular planar restricted three-body problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051898
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    ESCAPE OF PARTICLES ORBITING ASTEROIDS IN THE PRESENCE OF RADIATION PRESSURE THROUGH SEPARATRIX SPLITTING (1997)
    Springer
    Celestial mechanics and dynamical astronomy 67 (1997), S. 63-85 
    Details
    ISSN: 1572-9478
    Keywords: Asteroids ; radiation pressure ; Melnikov analysis ; Arnol'd diffusion.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the motion of grains in orbit around asteroids under the influence of radiation pressure originating in the flux of solar photons. Of interest is the possibility of initially bound grains becoming unbound and leaving the vicinity of the asteroid. The analysis extends the two-degree-of-freedom results of (Dankowicz, 1995) to three-degree-of-freedom motions. In particular, we use a Melnikov-type approach for finding transversal points of intersection between high-dimensional perturbed stable and unstable manifolds. As a consequence, the system is shown to be nonintegrable and the resulting homoclinic tangles are suggested as a means for phase space transport along resonance layers, so-called Arnol'd diffusion. We discuss the implications of the diffusion on the depletion of asteroid-bound particles and attempt to estimate the diffusion rate for physical comparison. For particular values of physical parameters the time scale is shown to be on the order of hundreds of orbital revolutions of the asteroid around the sun.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008201916186
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  • 3
    Electronic Resource
    Electronic Resource
    On the Successive Constraint Imposition Approach to Multibody Mechanisms (1999)
    Springer
    Multibody system dynamics 3 (1999), S. 267-286 
    Details
    ISSN: 1573-272X
    Keywords: analytical mechanics ; constraints ; d'Alembert's principle ; orthogonal complements ; chains ; recursivity ; induction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A method is described for the successive imposition of constraints on a free particle mechanism and the subsequent derivation of closed sets of differential equations for the evolution of the mechanism with time. Fundamental is the idea of ideal constraints as contained in d'Alembert's principle. In particular, it is shown how constraints may be added one or more at a time, thereby obtaining intermediate descriptions with more dynamic freedom than the final mechanism. As a simple example, it is shown that the rigid body is such an intermediate description. The method is also applied to the problem of a chain of n particles or n rigid rods. Both an inductive and a constructive approach are demonstrated in deriving the equations of motion for arbitrary n.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009886606941
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  • 4
    Electronic Resource
    Electronic Resource
    Some special orbits in the two-body problem with radiation pressure (1994)
    Springer
    Celestial mechanics and dynamical astronomy 58 (1994), S. 353-370 
    Details
    ISSN: 1572-9478
    Keywords: Two-body problem ; radiation pressure ; KS variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The motion has been studied of a particle in a gravitational field perturbed by radiation pressure. By combining the formulation in the physical space variables with the KS variables we obtained explicit evidence for the existence of a surface of stable circular orbits with centers on an axis through the primary body. Furthermore, the effects of a sharp shadow on the two-dimensional unstable parabolic orbits were investigated. It was found that they do not survive the introduction of a shadow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692010
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  • 5
    Electronic Resource
    Electronic Resource
    Evolving Control Strategies for Suppressing Heteroclinic Bursting (1999)
    Springer
    Dynamics and control 9 (1999), S. 149-171 
    Details
    ISSN: 1573-8450
    Keywords: Heteroclinic bursting ; O(2) ; turbulent boundary layer ; control ; genetic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We combine a detailed understanding of the dynamics of low-dimensional models of burstingin the turbulent boundary layer with the method of Genetic Programming to obtain appropriate control strategies for the suppressionof such bursting in these models. The study is applicable toO(2) symmetric systems for which structurally stable heteroclinic cycles are the dominant dynamical features. We argue that such a combined approach can prove a useful tool in achieving control in higher-dimensional models where actual analysis is prohibitively complicated. The results of the present study are compared to near-optimal controllers derived in previous studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008317829361
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  • 6
    Book
    Book
    Recipes for continuation / (2013)
    Philadelphia :Society for Industrial and Applied Mathematics,
    Details
    Title: Recipes for continuation /
    Author: Dankowicz, Harry
    Contributer: Schilder, Frank
    Publisher: Philadelphia :Society for Industrial and Applied Mathematics,
    Year of publication: 2013
    Pages: pages cm
    Series Statement: Computational science and engineering series
    ISBN: 978-1-611-97256-6
    Type of Medium: Book
    Language: English
    URL: http://www.zbmath.org/?q=an:06172086
    URL: http://www.loc.gov/catdir/enhancements/fy1310/2012046499-d.html
    URL: http://www.loc.gov/catdir/enhancements/fy1310/2012046499-t.html
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