Mechanics in Differential Geometry

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.

This course and reference book develops theoretical mechanics within the modern framework of differential geometry.
Foundations of differential geometry recalled in a rigorous and practical way as an unavoidable prerequisite make the work autonomous. Manifolds, tensors, exterior algebra, Lie derivative, Lie algebra, integration of forms, Riemannian geometry, and more refer to a previous author's book. Since manifold symplectic structure, canonical forms, brackets, etc. concern modern mechanics, symplectic geometry is an 'interlinking field'.
Lagrangian and Hamiltonian formalisms, with their own spaces and functions, start mechanics where fundamental principles, etc. are clearly situated given didactic comparisons, numerous diagrams,figures and solved exercises, as well as Hamilton-Jacobi theory, perturbations, stability, qualitative dynamics.
Statistical mechanics, celestial mechanics, etc., also a fluid-dynamical system , an original method with Fourier transforms deserve research.