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Geometric formulations of physical theories. Statics and dynamics of mechanical systems. (English) Zbl 0707.58001
Monographs and Textbooks in Physical Science, Lecture Notes, 11. Napoli: Bibliopolis. xii, 129 p. (1989).
The author starts with a review of differential geometry emphasizing the geometry of cotangent bundles. This geometrical basis is then used to formulate the principles of virtual work and virtual action applied to the statics and dynamics of mechanical systems.
The contents of these lecture notes are the following: (1) Differential manifolds, (2) Differential fibrations, (3) The tangent bundle of a manifold, (4) The cotangent bundle, (5) Differential forms, (6) Lagrangian submanifolds of the cotangent bundle, (7) Equilibrium of static systems, (8) Examples of static systems, (9) The tangent bundle of a vector bundle, (10) The iterated tangent bundle, (11) Bundles dual to the iterated tangent bundle, (12) Derivations of differential forms on the tangent bundle, (13) Lagrangian formulation of dynamics of mechanical systems, (14) Examples of Lagrangian systems, (15) Hamiltonian formulation of dynamics of mechanical systems, (16) Examples of Hamiltonian systems.
Reviewer: G.M.Rassias

MSC:
58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
57-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
70H05 Hamilton’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57R22 Topology of vector bundles and fiber bundles
55Rxx Fiber spaces and bundles in algebraic topology
70-XX Mechanics of particles and systems
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