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 : 4.22/5 ( download)

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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.

Author : Hamad M. Yehia
Publisher : Springer Nature
ISBN 13 : 3030963365
Total Pages : 473 pages
Book Rating : 4.61/5 ( download)

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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.

Author : Felix L. Chernousko
Publisher : Springer
ISBN 13 : 3319539280
Total Pages : 241 pages
Book Rating : 4.87/5 ( download)

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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 241 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.

Author : Jacques Bélair
Publisher : Springer
ISBN 13 : 3319303791
Total Pages : 806 pages
Book Rating : 4.96/5 ( download)

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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 806 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.

Author : Alexey Borisov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110542978
Total Pages : 783 pages
Book Rating : 4.74/5 ( download)

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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 783 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

Author : Giuseppe Grioli
Publisher : Springer Science & Business Media
ISBN 13 : 3642109918
Total Pages : 360 pages
Book Rating : 4.11/5 ( download)

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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.

Author : Tomáš Bodnár
Publisher : Birkhäuser
ISBN 13 : 3319602829
Total Pages : 519 pages
Book Rating : 4.20/5 ( download)

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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 519 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.

Author : Harley Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 1461395895
Total Pages : 194 pages
Book Rating : 4.98/5 ( download)

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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.

Author : Carlos M. Roithmayr
Publisher : Cambridge University Press
ISBN 13 : 1316060616
Total Pages : pages
Book Rating : 4.12/5 ( download)

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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 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.

Author : Peter C. Hughes
Publisher : Courier Corporation
ISBN 13 : 048614013X
Total Pages : 594 pages
Book Rating : 4.31/5 ( download)

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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.