Mathematical Methods Of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 9781475720631
Size: 10.95 MB
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Lineare Algebra 2

Author: Stefan Waldmann
Publisher: Springer-Verlag
ISBN: 9783662533482
Size: 20.34 MB
Format: PDF, Kindle
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In diesem Band des zweiteiligen Lehrbuchs zur Linearen Algebra werden zum einen verschiedene Anwendungen zu den Themen des ersten Bandes vertieft: es wird die Lösungstheorie linearer gewöhnlicher Differentialgleichungen mit konstanten Koeffizienten vorgestellt. Zum anderen werden die formalen Konzepte der linearen Algebra vertieft. Neben Quotientenkonstruktionen und der Theorie der symmetrischen und antisymmetrischen Bilinearformen wird vor allem die multilineare Algebra zusammen mit Tensorprodukten im Detail besprochen. Wie schon im ersten Band ist der Zugang dieses Lehrbuchs eher klassisch: Die formalen Aspekte der wissenschaftlichen Mathematik werden stark betont. Noch stärker als im ersten Band wird jedoch gerade aus den Anwendungen in der mathematischen Physik wichtige Motivation für das Vorgehen gewonnen. Auf diese Weise ist das Lehrbuch sowohl für Studierende der Mathematik als auch der Physik geeignet. Insgesamt über 100 umfangreiche Übungen erleichtern das Selbststudium. Der Inhalt von Band 2: Lineare Differentialgleichungen und die Exponentialabbildung Quotienten Multilineare Abbildungen und Tensorprodukte Bilinearformen und Quadriken Der Autor Stefan Waldmann studierte Physik in Freiburg, wo er 1999 promovierteund 2003 habilitierte. Nach Professuren für Differentialgeometrie inLeuven und harmonische Analysis in Erlangen ist er nun am Institut fürMathematik der Universität Würzburg Inhaber des Lehrstuhls für Mathematische Physik.

Geometric Continuum Mechanics And Induced Beam Theories

Author: Simon Eugster
Publisher: Springer
ISBN: 9783319164953
Size: 12.24 MB
Format: PDF, ePub
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This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

Essays In Mathematics And Its Applications

Author: Themistocles Rassias
Publisher: Springer
ISBN: 9783319313382
Size: 11.57 MB
Format: PDF, Mobi
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This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.

Introduction To Geometry Of Manifolds With Symmetry

Author: V.V. Trofimov
Publisher: Springer Science & Business Media
ISBN: 9789401719612
Size: 13.71 MB
Format: PDF
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One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.