Viva Books Private Limited
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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 method 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 operators, ....) 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, oneparameter 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, ...