Juan C. Simo's Books

Mechanics: From Theory to Computation

From Theory to Computation : Essays in Honor of Juan Carlos Simo : Papers Invited

By: Juan Carlos Simo

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Mechanics: From Theory to Computation

From Theory to Computation : Essays in Honor of Juan Carlos Simo : Papers Invited

By: Juan Carlos Simo

This collection of papers in honour of Juan-Carlos Simo cover subjects including: dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods; gravity waves on the surface of the sphere; and problems and progress in microswimming.

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546

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387986634

ISBN 13

9780387986630

Dynamics and Control of Multibody Systems

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 30-August 5, 1988, with Support from the National Science Foundation

By: Perinkulam Sambamurthy Krishnaprasad,Juan C. Simo

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Dynamics and Control of Multibody Systems

Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 30-August 5, 1988, with Support from the National Science Foundation

By: Perinkulam Sambamurthy Krishnaprasad,Juan C. Simo

The study of complex, interconnected mechanical systems with rigid and flexible articulated components is of growing interest to both engineers and mathematicians. Recent work in this area reveals a rich geometry underlying the mathematical models used in this context. In particular, Lie groups of symmetries, reduction, and Poisson structures play a significant role in explicating the qualitative properties of multibody systems. In engineering applications, it is important to exploit the special structures of mechanical systems. For example, certain mechanical problems involving control of interconnected rigid bodies can be formulated as Lie-Poisson systems. The dynamics and control of robotic, aeronautic, and space structures involve difficulties in modeling, mathematical analysis, and numerical implementation. For example, a new generation of spacecraft with large, flexible components are presenting new challenges to the accurate modeling and prediction of the dynamic behavior of such structures. Recent developments in Hamiltonian dynamics and coupling of systems with symmetries has shed new light on some of these issues, while engineering questions have suggested new mathematical structures. These kinds of considerations motivated the organization of the AMS-IMS-SIAM Joint Summer Research Conference on Control Theory and Multibody Systems, held at Bowdoin College in August, 1988. This volume contains the proceedings of that conference. The papers presented here cover a range of topics, all of which could be viewed as applications of geometrical methods to problems arising in dynamics and control. The volume contains contributions from some of the top researchers and provides an excellent overview of the frontiers of research in this burgeoning area.

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Page Count

488

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851047

ISBN 13

9780821851043

Differential Galois Theory and Non-Integrability of Hamiltonian Systems

By: Juan J. Morales Ruiz

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Differential Galois Theory and Non-Integrability of Hamiltonian Systems

By: Juan J. Morales Ruiz

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincaré and Lyapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Hénon-Heiles system, etc. The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simó, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed. - - - The book is an excellent introduction to non-integrability methods in Hamiltonian mechanics and brings the reader to the forefront of research in the area. The inclusion of a large number of worked-out examples, many of wide applied interest, is commendable. There are many historical references, and an extensive bibliography. (Mathematical Reviews) For readers already prepared in the two prerequisite subjects [differential Galois theory and Hamiltonian dynamical systems], the author has provided a logically accessible account of a remarkable interaction between differential algebra and dynamics. (Zentralblatt MATH)

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Page Count

177

Publisher

Birkhäuser

Published Date

ISBN 10

3034887183

ISBN 13

9783034887182

Geometry and Dynamics of Integrable Systems

By: Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung

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Geometry and Dynamics of Integrable Systems

By: Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

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Page Count

148

Publisher

Birkhäuser

Published Date

ISBN 10

3319335030

ISBN 13

9783319335032

The Porous Medium Equation

Mathematical Theory

By: Juan Luis Vazquez

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The Porous Medium Equation

Mathematical Theory

By: Juan Luis Vazquez

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heatequation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, andother fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.

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Page Count

647

Publisher

Oxford University Press

Published Date

ISBN 10

0198569033

ISBN 13

9780198569039

Book's by Juan C. Simo

Mechanics: From Theory to Computation

Mechanics: From Theory to Computation

Dynamics and Control of Multibody Systems

Dynamics and Control of Multibody Systems

Differential Galois Theory and Non-Integrability of Hamiltonian Systems

Differential Galois Theory and Non-Integrability of Hamiltonian Systems

Geometry and Dynamics of Integrable Systems

Geometry and Dynamics of Integrable Systems

The Porous Medium Equation

The Porous Medium Equation

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