The General Problem Of The Motion Of Coupled Rigid Bodies About A Fixed Point

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The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point

Author : Eugene Leimanis
Publisher : Springer Science & Business Media
ISBN 13 : 3642884121
Total Pages : 352 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point by : Eugene Leimanis

Download or read book The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point written by Eugene Leimanis and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.

Rigid Body Dynamics

Author : Hamad M. Yehia
Publisher : Springer Nature
ISBN 13 : 3030963365
Total Pages : 473 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Rigid Body Dynamics by : Hamad M. Yehia

Download or read book Rigid Body Dynamics written by Hamad M. Yehia and published by Springer Nature. This book was released on 2022-06-27 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a complete and up-to-date examination of rigid body dynamics using a Lagrangian approach. All known integrable cases, which were previously scattered throughout the literature, are collected here for convenient reference. Also contained are particular solutions to diverse problems treated within rigid body dynamics. The first seven chapters introduce the elementary dynamics of the rigid body and its main problems. A full historical account of the discovery and development of each of the integrable cases is included as well. Instructors will find this portion of the book well-suited for an undergraduate course, having been formulated by the author in the classroom over many years. The second part includes more advanced topics and some of the author’s original research, highlighting several unique methods he developed that have led to significant results. Some of the specific topics covered include the twelve known solutions of the equations of motion in the classical problem, which has not previously appeared in English before; a collection of completely new integrable cases; and the motion of a rigid body around a fixed point under the action of an asymmetric combination of potential and gyroscopic forces. Rigid Body Dynamics will appeal to researchers in the area as well as those studying dynamical and integrable systems theory.

Evolution of Motions of a Rigid Body About its Center of Mass

Author : Felix L. Chernousko
Publisher : Springer
ISBN 13 : 3319539280
Total Pages : 270 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Evolution of Motions of a Rigid Body About its Center of Mass by : Felix L. Chernousko

Download or read book Evolution of Motions of a Rigid Body About its Center of Mass written by Felix L. Chernousko and published by Springer. This book was released on 2017-04-20 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approach based on the averaging procedure is applicable to bodies with arbitrary ellipsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.

Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author : Jacques Bélair
Publisher : Springer
ISBN 13 : 3319303791
Total Pages : 777 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Mathematical and Computational Approaches in Advancing Modern Science and Engineering by : Jacques Bélair

Download or read book Mathematical and Computational Approaches in Advancing Modern Science and Engineering written by Jacques Bélair and published by Springer. This book was released on 2016-08-10 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science and engineering. It provides a primary and ubiquitous tool in the context making new discoveries, as well as in the development of new theories and techniques for solving key problems arising in scientific and engineering applications. The contributions, which are the product of two highly successful meetings held jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid Laurier University in June 2015, i.e. the International Conference on Applied Mathematics, Modeling and Computational Science, and the Annual Meeting of the Canadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interested in a broader overview of the methods, ideas and tools involved in mathematical and computational approaches developed for other disciplines, including the natural and social sciences, engineering and technology.

Rigid Body Dynamics

Author : Alexey Borisov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311054444X
Total Pages : 530 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Rigid Body Dynamics by : Alexey Borisov

Download or read book Rigid Body Dynamics written by Alexey Borisov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-12-03 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

Stereodynamics

Author : Giuseppe Grioli
Publisher : Springer Science & Business Media
ISBN 13 : 3642109918
Total Pages : 360 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Stereodynamics by : Giuseppe Grioli

Download or read book Stereodynamics written by Giuseppe Grioli and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: G. Grioli: Particular solutions in stereodynamics.- P. Hagedorn: On the converse of the Lagrange-Dirichlet stability theorem.- M. Langlois: Contribution à l’étude du mouvement du corps rigide à n dimensions autour d’un point fixe.- E. Leimanis: Some recent results concerning the motion of a rigid body about a fixed point.- H. Price: A canonical form of Euler’s equations and a method of solutions for arbitrary applied couples.- V.V. Rumyentsev: Dynamics and stability of rigid bodies.- J. Wittenburg: The dynamics of systems of coupled rigid bodies. A new general formalism with applications.

Particles in Flows

Author : Tomáš Bodnár
Publisher : Birkhäuser
ISBN 13 : 3319602829
Total Pages : 526 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Particles in Flows by : Tomáš Bodnár

Download or read book Particles in Flows written by Tomáš Bodnár and published by Birkhäuser. This book was released on 2017-09-30 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to face particles in flows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from deep mathematical analysis of the associated models, through the techniques of their numerical solution, towards real applications and physical implications. The scope and structure of the book as well as the selection of authors was motivated by the very successful summer course and workshop "Particles in Flows'' that was held in Prague in the August of 2014. This meeting revealed the need for a book dealing with this specific and challenging multidisciplinary subject, i.e. particles in industrial, environmental and biomedical flows and the combination of fluid mechanics, solid body mechanics with various aspects of specific applications.

The Theory of Pseudo-rigid Bodies

Author : Harley Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 1461395895
Total Pages : 194 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis The Theory of Pseudo-rigid Bodies by : Harley Cohen

Download or read book The Theory of Pseudo-rigid Bodies written by Harley Cohen and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph concerns the development, analysis, and application of the theory of pseudo-rigid bodies. It collects together our work on that subject over the last five years. While some results have appeared else where, much of the work is new. Our objective in writing this mono graph has been to present a new theory of the deformation of bodies, one that has not only a firm theoretical basis, but also the simplicity to serve as an effective tool in practical problems. Consequently, the main body of the treatise is a multifaceted development of the theory, from foundations to explicit solutions to linearizations to methods of approximation. The fact that this variety of aspects, each examined in considerable detail, can be collected together in a single, unified treat ment gives this theory an elegance that we feel sets it apart from many others. While our goal has always been to give a complete treatment of the theory as it now stands, the work here is not meant to be definitive. Theories are not entities that appear suddenly one day and thereafter stand as given. Rather, they must mature and grow with time and experience. Our development is more correctly a beginning, tempting others to explore, appraise, and modify its features so as to produce something better.

Mechanics Day

Author : W. F. Shadwick
Publisher : American Mathematical Soc.
ISBN 13 : 0821802615
Total Pages : 271 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mechanics Day by : W. F. Shadwick

Download or read book Mechanics Day written by W. F. Shadwick and published by American Mathematical Soc.. This book was released on 1996 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial diffe.

Dynamics

Author : Carlos M. Roithmayr
Publisher : Cambridge University Press
ISBN 13 : 1316060616
Total Pages : 528 pages
Book Rating : 4.3/5 (16 download)

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Book Synopsis Dynamics by : Carlos M. Roithmayr

Download or read book Dynamics written by Carlos M. Roithmayr and published by Cambridge University Press. This book was released on 2016-03-09 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is ideal for teaching students in engineering or physics the skills necessary to analyze motions of complex mechanical systems such as spacecraft, robotic manipulators, and articulated scientific instruments. Kane's method, which emerged recently, reduces the labor needed to derive equations of motion and leads to equations that are simpler and more readily solved by computer, in comparison to earlier, classical approaches. Moreover, the method is highly systematic and thus easy to teach. This book is a revision of Dynamics: Theory and Applications (1985), by T. R. Kane and D. A. Levinson, and presents the method for forming equations of motion by constructing generalized active forces and generalized inertia forces. Important additional topics include approaches for dealing with finite rotation, an updated treatment of constraint forces and constraint torques, an extension of Kane's method to deal with a broader class of nonholonomic constraint equations, and other recent advances.

Spacecraft Attitude Dynamics

Author : Peter C. Hughes
Publisher : Courier Corporation
ISBN 13 : 048614013X
Total Pages : 594 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Spacecraft Attitude Dynamics by : Peter C. Hughes

Download or read book Spacecraft Attitude Dynamics written by Peter C. Hughes and published by Courier Corporation. This book was released on 2012-05-23 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive coverage includes environmental torques, energy dissipation, motion equations for four archetypical systems, orientation parameters, illustrations of key concepts with on-orbit flight data, and typical engineering hardware. 1986 edition.

Space Vehicle Dynamics and Control

Author : Bong Wie
Publisher : AIAA
ISBN 13 : 9781563472619
Total Pages : 692 pages
Book Rating : 4.4/5 (726 download)

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Book Synopsis Space Vehicle Dynamics and Control by : Bong Wie

Download or read book Space Vehicle Dynamics and Control written by Bong Wie and published by AIAA. This book was released on 1998 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook that incorporates the latest methods used for the analysis of spacecraft orbital, attitude, and structural dynamics and control. Spacecraft dynamics is treated as a dynamic system with emphasis on practical applications, typical examples of which are the analysis and redesign of the pointing control system of the Hubble Space Telescope and the analysis of an active vibrations control for the COFS (Control of Flexible Structures) Mast Flight System. In addition to the three subjects mentioned above, dynamic systems modeling, analysis, and control are also discussed. Annotation copyrighted by Book News, Inc., Portland, OR

Dynamics of Multibody Systems

Author : K. Magnus
Publisher : Springer Science & Business Media
ISBN 13 : 3642864619
Total Pages : 392 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Dynamics of Multibody Systems by : K. Magnus

Download or read book Dynamics of Multibody Systems written by K. Magnus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to a proposal made in 1974 by the Gesell schaft fUr Angewandte Mathematik und Mechanik (GAMM) the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) decided in 1975 to sponsor an international symposium on "Dynamics of Multibody Systems". A Scientific Committee has been appointed consisting of J.D.C. Crisp, Australia, T.R. Kane, USA, D.M. Klimov, USSR, A.D. De Pater, Netherlands, K. Magnus, Germany (chairman). This committee selected the participants to be invited and the papers to be presented at the symposium. As a result of this process 82 active scientific partici pants from 15 countries followed the invitation and 29 papers were presented. They are collected in this volume. At the symposium an additional presentation was delivered: Mrs. E. Gottzein introduced and ex plained a recently completed scientific movie on mag netic levitated vehicles. The aim of the symposium was the exchange of ideas and the discussion of methods and results in the field of Multibody Dynamics. This has been achieved by a really efficient scientific and social progr~m, organ ized for the six symposium days by a Local Organizing Committee. Members of this Committee were: S. Ballout, M. Lippmann, P.C. MUller, W.O. Schiehlen, G. Schweitzer, E. Truckenbrodt, K. Magnus (chair man) and members of the staff of the Institute of Mechanics.

Interactions Between Physics and Dynamics of Solar System Bodies

Author : E. Bois
Publisher : Springer Science & Business Media
ISBN 13 : 9401119023
Total Pages : 416 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Interactions Between Physics and Dynamics of Solar System Bodies by : E. Bois

Download or read book Interactions Between Physics and Dynamics of Solar System Bodies written by E. Bois and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fans of "Asterix the Gallic" know well that the only fear of people in Brittany is that the sky falls upon their head. So it must have been a shock for them (the fans of Asterix) to learn that a horde of Physicists and Dynamicists (some of them being actually Roman - ils sont fous ces Romains!) invaded the bay of Saint-Brieuc and spend a full week conjuring all the nastiness that the sky has in reserve, revelling in the horrors hidden beyond the blue dome; they talked with delight about "asteroids", "comets" and "meteor streams"; they grinned at the idea of "artificial satellites", these pots and pans of space always ready to fall upon you; some of them said strange things about the Moon, the planets, and evoked the "rings" of Saturn or of some other of their gods. One evening, a Roman from Pisa went as far as cornering some inhabitants in the large hut they used for their witchcraft and filled them with terror by describing the fate of the poor dinosaurs victims of a particularly nasty asteroid (or was it a comet?). You will be surprized to learn that Bretons did not exact a spectacular revenge for these offenses. On the contrary.

Perspectives in Dynamical Systems III: Control and Stability

Author : Jan Awrejcewicz
Publisher : Springer Nature
ISBN 13 : 3030773140
Total Pages : 355 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Perspectives in Dynamical Systems III: Control and Stability by : Jan Awrejcewicz

Download or read book Perspectives in Dynamical Systems III: Control and Stability written by Jan Awrejcewicz and published by Springer Nature. This book was released on 2021-12-14 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems. The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

Classical and Quantum Models and Arithmetic Problems

Author : Chudnovsky
Publisher : Routledge
ISBN 13 : 1351460544
Total Pages : 490 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Classical and Quantum Models and Arithmetic Problems by : Chudnovsky

Download or read book Classical and Quantum Models and Arithmetic Problems written by Chudnovsky and published by Routledge. This book was released on 2018-10-08 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an unsurpassed resource-important accounts of a variety of dynamic systems topicsrelated to number theory. Twelve distinguished mathematicians present a rare complete analyticsolution of a geodesic quantum problem on a negatively curved surface ... and explicitdetermination of modular function growth near a real point .. . applications of number theoryto dynamical systems and applications of mathematical physics to number theory . ..tributes to the often-unheralded pioneers in the field ... an examination of completely integrableand exactly solvable physical models .. . and much more!Classical and Quantum Models and Arithmetic Problems is certainly a major source of information,advancing the studies of number theorists, algebraists, and mathematical physicistsinterested in complex mathematical properties of quantum field theory, statistical mechanics,and dynamic systems. Moreover, the volume is a superior source of supplementary readingfor graduate-level courses in dynamic systems and application of number theory .

Classical and Celestial Mechanics

Author : Hildeberto Cabral
Publisher : Princeton University Press
ISBN 13 : 0691222487
Total Pages : 408 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Classical and Celestial Mechanics by : Hildeberto Cabral

Download or read book Classical and Celestial Mechanics written by Hildeberto Cabral and published by Princeton University Press. This book was released on 2020-12-08 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics. Because of the high quality of the results and the general interest in the lecturers' topics, the editors have assembled nine of the lectures here in order to make them available to mathematicians and students around the world. The material presented includes a good balance of pure and applied research and of complete and incomplete results. Bringing together material that is otherwise quite scattered in the literature and including some important new results, it will serve graduate students and researchers interested in Hamiltonian dynamics and celestial mechanics. The contributors are Dieter Schmidt, Ernesto Pérez-Chavela, Mark Levi, Plácido Táboas and Jack Hale, Jair Koiller et al., Hildeberto Cabral, Florin Diacu, and Alain Albouy. The topics covered include central configurations and relative equilibria for the N-body problem, singularities of the N-body problem, the two-body problem, normal forms of Hamiltonian systems and stability of equilibria, applications to celestial mechanics of Poincaré's compactification, the motion of the moon, geometrical methods in mechanics, momentum maps and geometric phases, holonomy for gyrostats, microswimming, and bifurcation from families of periodic solutions.