Mechanics (Tensors and Virtual Works)

Yves R Talpaert

Verlag: Viva Books Private Limited, 2008
ISBN 10: 8130909405 / ISBN 13: 9788130909400
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Beschreibung:

Mechanics, Tensors & Virtual Works is designated to be used for a first one-semester course in Mechanics at the upper undergraduate level. It is intended for third year students in mathematics, physics and engineering. Most of the text comes from this level courses that the author taught at universities and engineering schools. In the particular case where such a course cannot be taught to engineers, a lot of introduced matters constitute the mathematical and mechanical bases of applied engineering mechanics. The various chapters connect the notions of mechanics of first and second year with the ones which are developed in more specialized subjects as continuum mechanics at first, and fluid-dynamics, quantum mechanics, special relativity, general relativity, electromagnetism, stellar dynamics, celestial mechanics, meteorology, applied differential geometry, and so on. Mechanics, Tensors and Virtual Works is designed for the second part of an intermediate course in mechanics at the undergraduate level in mathematics and physics, and engineering too. Given its high level of pedagogy and numerous solved problems, this is also suitable for self-taught people having a background of theoretical mechanics. This course of Analytical Mechanics is the ideal mathematical and mechanical preparation for physics disciplines as continuum mechanics, fluid-dynamics, special relativity, general relativity, celestial mechanics, quantum mechanics?? The Virtual Work methods in Static and Tensors are introduced mathematical "tools" which give the mechanics treated subjects a great unity. So, Mass Geometry, Inertia Tensor, Kinetics and Dynamics of Systems are developed in the tensor context. The intensive use of the tensor calculus (with dual space, canonical isomorphism, exterior algebra, metric, covariant derivatives, volume form and adjoint, differential operations,?) contributes to reduce the gap between first and second academic cycles. Compiling data on Lagrangian Dynamics and Variational Principles, this book thoroughly covers d?Alembert-Lagrange principle, Lagrange?s equations, adjoint Lagrangian and first integrals, Euler equations, Hamilton?s variational principle, one-parameter group of diffeomorphisms, Euler-Noether theorem,? Also Hamiltonian Mechanics with N-body problem, Legendre transformation and Hamiltonian canonical equations, Liouville?s theorem in statistical mechanics, Largange and Poisson brackets, canonical transformations, Hamilton-Jacobi equation, separability,? Contents: REQUIREMENTS ? Point space and vector space: Point space (or affine space); Frame of reference and basis ? Dynams: Dynam definition and reduction elements; Properties and operations on dynams; Dynam of velocities; Acceleration vectors; Sliding velocity; Exercises ? STATICS ? Classic method: Mechanical actions; Classification of forces; Equilibrium conditions; Types of equilibrium of rigid bodies and structures; Stress and contact dynam; Types of constraints; Free-body diagram ? Method of virtual work: Number of degrees of freedom and generalized coordinates; Virtual displacements and virtual velocities; Virtual work; Exercises ? TENSORS ? First steps with tensors: Multilinear forms; Dual space, vectors and covectors; Tensors and tensor product ? Operations on tensors: Tensor algebra; Contraction and tensor criteria ? Euclidean vector space: Pre-Euclidean vector space; Canonical isomorphism and conjugate tensor; Euclidean vector spaces ? Exterior algebra: p-forms; q-vectors ? Point Spaces: Point space and natural frame; Tensor fields and metric element; Christoffel symbols; Absolute differential, covariant derivate, geodesic; Volume form and adjoint; Differential operators; Exercises ? MASS GEOMETRY AND INERTIA TENSOR ? Mass distribution and integrals: Density; Integrals of real-valued functions and vector funct Printed Pages: 474. Buchnummer des Verkäufers 5159

Bibliografische Details

Titel: Mechanics (Tensors and Virtual Works)
Verlag: Viva Books Private Limited
Erscheinungsdatum: 2008
Einband: Hardcover
Zustand: New
Auflage: First edition.

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