Canonical Floquet Perturbation Theory
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Canonical Floquet Perturbation Theory
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Author : David J. Pohlen (CAPT, USAF.)
language : en
Publisher:
Release Date : 1992
Canonical Floquet Perturbation Theory written by David J. Pohlen (CAPT, USAF.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Floquet theory categories.
Canonical Floquet Perturbation Theory
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Author :
language : en
Publisher:
Release Date : 1992
Canonical Floquet Perturbation Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Classical Floquet theory is examined in order to generate a canonical transformation to modal variables for periodic system This transformation is considered canonical if the periodic matrix of eigenvectors is symplectic at the initial time. Approaches for symplectic normalization of the eigenvectors had to be examined for each of the different Poincare eigenvalue cases. Particular attention was required in the degenerate case, which depended on the solution of a generalized eigenvector. Transformation techniques to ensure real modal variables and real periodic eigenvectors were also needed. Periodic trajectories in the restricted three-body case were then evaluated using the canonical Floquet solution. The system used for analyses is the Sun-Jupiter system. This system was especially useful since it contained two of the more difficult Poincare eigenvalue cases, the degenerate case and the imaginary eigenvalue case. The perturbation solution to the canonical modal variables was examined using both an expansion of the Hamiltonian and using a representation that was considered exact Both methods compared quite well for small perturbations to the initial condition. As expected, the expansion solution failed first due to truncation after the third order term of the expansion.
The Modal Solution To The Moon S Orbit Using Canonical Floquet Perturbation Theory
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Author :
language : en
Publisher:
Release Date : 1993
The Modal Solution To The Moon S Orbit Using Canonical Floquet Perturbation Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Using the restricted three body problem, the equations of motion (EOM) and Hamiltonian are computed for the moon's orbit in physical variables. A periodic orbit is found in the vicinity of the moon's orbit, and classical Floquet theory is applied to the periodic orbit to give stability information and the complete solution to the equations of variation. Floquet theory also supplies a transformation from physical variables to modal variables. This transformation to modal variables is made canonical by constraining the initial transformation matrix to be symplectic. Actual lunar data is used to calculate the modes for the real moon's orbit. Once satisfied that the moon's real-world modes are in (or near) the linear regime of the periodic orbit, the modal EOM are found by doing a perturbation expansion on the new modal Hamiltonian. The modal results from the real lunar orbit are compared with the modal EOM/ expansion results. The modal expansion proves to be an accurate solution to the moon's orbit given enough expansion terms.
Canonical Perturbation Theories
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Author : Sylvio Ferraz-Mello
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-30
Canonical Perturbation Theories written by Sylvio Ferraz-Mello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-30 with Science categories.
The book is written mainly to advanced graduate and post-graduate students following courses in Perturbation Theory and Celestial Mechanics. It is also intended to serve as a guide in research work and is written in a very explicit way: all perturbation theories are given with details allowing its immediate application to real problems. In addition, they are followed by examples showing all steps of their application.
The Application Of Floquet Theory To The Computation Of Small Orbital Perturbations Over Long Time Intervals Using The Tschauner Hempel Equations
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Author : Robert Gillon Smith
language : en
Publisher:
Release Date : 1965
The Application Of Floquet Theory To The Computation Of Small Orbital Perturbations Over Long Time Intervals Using The Tschauner Hempel Equations written by Robert Gillon Smith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Artificial satellites categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Physics Of Particle Accelerators
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Author : Margaret Dienes
language : en
Publisher:
Release Date : 1989
Physics Of Particle Accelerators written by Margaret Dienes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Batavia, IL categories.
Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Masters Theses In The Pure And Applied Sciences
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Author : Wade H. Shafer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Masters Theses In The Pure And Applied Sciences written by Wade H. Shafer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Masters Theses in the Pure and Applied Sciences was first conceived, published, and disseminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS)* at Purdue University in 1957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dis semination phases of the activity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thought that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all concerned if the printing and distribution of the volumes were handled by an international publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Corporation of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 38 (thesis year 1993) a total of 13,787 thesis titles from 22 Canadian and 164 United States universities. We are sure that this broader base for these titles reported will greatly enhance the value of this impor tant annual reference work. While Volume 38 reports theses submitted in 1993, on occasion, certain uni versities do report theses submitted in previous years but not reported at the time.
Adiabatic Perturbation Theory In Quantum Dynamics
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Author : Stefan Teufel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Adiabatic Perturbation Theory In Quantum Dynamics written by Stefan Teufel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Perturbation (Quantum dynamics) categories.