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1 Yu, Yang Orbital Dynamics in the Gravitational Field of Small Bodies I10386 2016 eBook  
2 Mart??nez-Guerra, Rafael Algorithms of Estimation for Nonlinear Systems I09780 2017 eBook  
3 G??mez, Gerard Astrodynamics Network AstroNet-II I09777 2016 eBook  
4 Valtonen, Mauri The Three-body Problem from Pythagoras to Hawking I09766 2016 eBook  
5 Scheck, Florian Mechanics I09673 2018 eBook  
6 L??ber, Jakob Optimal Trajectory Tracking of Nonlinear Dynamical Systems I09534 2017 eBook  
7 Arutyunov, Gleb Elements of Classical and Quantum Integrable Systems I09392 2019 eBook  
8 Luo, Albert C. J Bifurcation Dynamics in Polynomial Discrete Systems I09327 2020 eBook  
9 Shevchenko, Ivan I The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy I09238 2017 eBook  
10 Conte, Robert The Painlev?? Handbook I09128 2020 eBook  
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TitleOrbital Dynamics in the Gravitational Field of Small Bodies
Author(s)Yu, Yang
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2016.
DescriptionXVIII, 123 p. 49 illus., 17 illus. in color : online resource
Abstract NoteThis prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs), which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the results prove to be both revealing and pervasive for a large group of SSSBs.
ISBN,Price9783662526934
Keyword(s)1. Aerospace engineering 2. Aerospace Technology and Astronautics 3. Applications of Nonlinear Dynamics and Chaos Theory 4. ASTRONAUTICS 5. ASTROPHYSICS 6. Astrophysics and Astroparticles 7. CLASSICAL MECHANICS 8. COMPUTER SIMULATION 9. Dynamical Systems and Ergodic Theory 10. DYNAMICS 11. EBOOK 12. EBOOK - SPRINGER 13. ERGODIC THEORY 14. MECHANICS 15. Simulation and Modeling 16. STATISTICAL PHYSICS
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TitleAlgorithms of Estimation for Nonlinear Systems : A Differential and Algebraic Viewpoint
Author(s)Mart??nez-Guerra, Rafael;Cruz-Ancona, Christopher Diego
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXX, 197 p. 58 illus., 10 illus. in color : online resource
Abstract NoteThis book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms
ISBN,Price9783319530406
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. DYNAMICAL SYSTEMS 3. Dynamical Systems and Ergodic Theory 4. DYNAMICS 5. EBOOK 6. EBOOK - SPRINGER 7. ERGODIC THEORY 8. STATISTICAL PHYSICS 9. Statistical Physics and Dynamical Systems 10. VIBRATION 11. Vibration, Dynamical Systems, Control
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TitleAstrodynamics Network AstroNet-II : The Final Conference
Author(s)G??mez, Gerard;Masdemont, Josep J
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXVIII, 325 p. 180 illus., 159 illus. in color : online resource
Abstract NoteThese are the proceedings of the "AstroNet-II International Final Conference". This conference was one of the last milestones of the Marie-Curie Research Training Network on Astrodynamics "AstroNet-II", that has been funded by the European Commission under the Seventh Framework Programme. The aim of the conference, and thus??this book,??is to communicate work on astrodynamics problems??to an international and specialised audience. The??results are??presented by both members of the network and??invited specialists. The topics include: trajectory design and control, attitude control, structural flexibility of spacecraft and formation flying. The book addresses a readership across the traditional boundaries between mathematics, engineering and industry by offering an interdisciplinary and multisectorial overview of the field
ISBN,Price9783319239866
Keyword(s)1. Aerospace engineering 2. Aerospace Technology and Astronautics 3. ASTRONAUTICS 4. Dynamical Systems and Ergodic Theory 5. DYNAMICS 6. EBOOK 7. EBOOK - SPRINGER 8. ERGODIC THEORY 9. SPACE SCIENCES 10. Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)
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TitleThe Three-body Problem from Pythagoras to Hawking
Author(s)Valtonen, Mauri;Anosova, Joanna;Kholshevnikov, Konstantin;Myll??ri, Aleksandr;Orlov, Victor;Tanikawa, Kiyotaka
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXI, 173 p. 96 illus., 70 illus. in color : online resource
Abstract NoteThis book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today???s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal gravitation was discovered by Newton, it became immediately a problem to understand why these three-bodies form a stable system, in spite of the pull exerted from one to the other. In fact, it was a big question whether this system is stable at all in the long run. Leading mathematicians attacked this problem over more than two centuries without arriving at a definite answer. The introduction of computers in the last half-a-century has revolutionized the study; now many answers have been found while new questions about the three-body problem have sprung up. One of the most recent developments has been in the treatment of the problem in Einstein???s General Relativity, the new theory of gravitation which is an improvement on Newton???s theory. Now it is possible to solve the problem for three black holes and to test one of the most fundamental theorems of black hole physics, the no-hair theorem, due to Hawking and his co-workers
ISBN,Price9783319227269
Keyword(s)1. ASTRONOMY 2. ASTROPHYSICS 3. Astrophysics and Astroparticles 4. Classical and Quantum Gravitation, Relativity Theory 5. CLASSICAL MECHANICS 6. Dynamical Systems and Ergodic Theory 7. DYNAMICS 8. EBOOK 9. EBOOK - SPRINGER 10. ERGODIC THEORY 11. GRAVITATION 12. Mathematical Methods in Physics 13. MECHANICS 14. PHYSICS 15. Popular Science in Astronomy
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TitleMechanics : From Newton's Laws to Deterministic Chaos
Author(s)Scheck, Florian
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2018.
DescriptionXVII, 591 p. 175 illus : online resource
Abstract NoteThis book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new??sections on applications in science. ?? Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. ?? The book contains more than 150 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics
ISBN,Price9783662554906
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. CLASSICAL MECHANICS 4. Dynamical Systems and Ergodic Theory 5. DYNAMICS 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MATHEMATICS 9. ERGODIC THEORY 10. MECHANICS 11. Mechanics, Applied 12. Theoretical and Applied Mechanics
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TitleOptimal Trajectory Tracking of Nonlinear Dynamical Systems
Author(s)L??ber, Jakob
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXIV, 243 p. 36 illus., 32 illus. in color : online resource
Abstract NoteBy establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry
ISBN,Price9783319465746
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. CALCULUS OF VARIATIONS 3. Calculus of Variations and Optimal Control; Optimization 4. DYNAMICAL SYSTEMS 5. Dynamical Systems and Ergodic Theory 6. DYNAMICS 7. EBOOK 8. EBOOK - SPRINGER 9. ERGODIC THEORY 10. STATISTICAL PHYSICS 11. VIBRATION 12. Vibration, Dynamical Systems, Control
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TitleElements of Classical and Quantum Integrable Systems
Author(s)Arutyunov, Gleb
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2019.
DescriptionXIII, 414 p. 51 illus., 20 illus. in color : online resource
Abstract NoteIntegrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible
ISBN,Price9783030241988
Keyword(s)1. CLASSICAL MECHANICS 2. Dynamical Systems and Ergodic Theory 3. DYNAMICS 4. EBOOK 5. EBOOK - SPRINGER 6. ERGODIC THEORY 7. MATHEMATICAL PHYSICS 8. MECHANICS 9. STATISTICAL PHYSICS 10. Statistical Physics and Dynamical Systems
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TitleBifurcation Dynamics in Polynomial Discrete Systems
Author(s)Luo, Albert C. J
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2020.
DescriptionXI, 430 p. 68 illus., 66 illus. in color : online resource
Abstract NoteThis is the first book focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems. It comprehensively discusses the general mathematical conditions of bifurcations in polynomial nonlinear discrete systems, as well as appearing and switching bifurcations for simple and higher-order singularity period-1 fixed-points in the 1-dimensional polynomial discrete systems. Further, it analyzes the bifurcation trees of period-1 to chaos generated by period-doubling, and monotonic saddle-node bifurcations. Lastly, the book presents methods for period-2 and period-doubling renormalization for polynomial discrete systems, and describes the appearing mechanism and period-doublization of period-n fixed-points on bifurcation trees for the first time, offering readers fascinating insights into recent research results in nonlinear discrete systems
ISBN,Price9789811552083
Keyword(s)1. COMPLEXITY 2. COMPUTATIONAL COMPLEXITY 3. Control and Systems Theory 4. Control engineering 5. DYNAMICAL SYSTEMS 6. Dynamical Systems and Ergodic Theory 7. DYNAMICS 8. EBOOK 9. EBOOK - SPRINGER 10. ERGODIC THEORY 11. VIBRATION 12. Vibration, Dynamical Systems, Control
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TitleThe Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy
Author(s)Shevchenko, Ivan I
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXI, 194 p. 39 illus., 8 illus. in color : online resource
Abstract NoteThis book deals with an effect in celestial mechanics that has become quite important in exoplanet research. The Lidov-Kozai effect reveals itself in coherent periodic variations (which can be very large) of the inclination and eccentricity of an orbiting body in the presence of an inclined perturber. The effect is known to be important in the motion of many asteroids and planetary satellites. What is more, now it attracts more and more interest in the astronomical and astrophysical community due to its relevance for many exoplanetary systems. Recent years witnessed major advancements in its theory. It would be no exaggeration to say that nowadays the Lidov-Kozai effect becomes one of the most studied astrophysical effects. This book covers the multitude of the Lidov-Kozai effect???s modern applications and its theory developments. It will be useful for researchers and students working in astrophysics, celestial mechanics, stellar dynamics, theoretical mechanics, space missions design, depending on the interests of the reader. The book is self-contained. It provides the full detailed coverage of the effect???s theory and applications
ISBN,Price9783319435220
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. ASTROPHYSICS 3. Astrophysics and Astroparticles 4. Dynamical Systems and Ergodic Theory 5. DYNAMICS 6. EBOOK 7. EBOOK - SPRINGER 8. ERGODIC THEORY 9. PLANETOLOGY 10. SPACE SCIENCES 11. Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) 12. STATISTICAL PHYSICS
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TitleThe Painlev?? Handbook
Author(s)Conte, Robert;Musette, Micheline
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXXXI, 389 p. 15 illus., 6 illus. in color : online resource
Abstract NoteThis book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlev?? test and shows how Painlev?? analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schr??dinger equation, the Korteweg-de Vries equation, H??non-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlev?? function; and an overview of new results since the book???s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences
ISBN,Price9783030533403
Keyword(s)1. APPLIED MATHEMATICS 2. Chemometrics 3. Dynamical Systems and Ergodic Theory 4. DYNAMICS 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. ERGODIC THEORY 9. Math. Applications in Chemistry 10. Mathematical and Computational Engineering 11. Mathematical Methods in Physics 12. MATHEMATICAL PHYSICS 13. PARTIAL DIFFERENTIAL EQUATIONS 14. PHYSICS
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