Lagrangian and Hamiltonian geometries. Applications to Mechanics free ebook download.

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Lagrangian and Hamiltonian geometries. Applications to Mechanics free ebook download

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Mathematics

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Author(s):	Miron Radu

Date:	2015	Format:	PDF	Language:	English	ISBN/ASIN:	3659710199
Pages:	1	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	8/5/2020 6:36:27 PM

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The purpose of this book is to provide a presentation of the geometrical theory of Lagrange and Hamilton spaces of order k, greater or equal to 1, as well as to define and investigate some new Analytical Mechanics. It is shown that a rigorous geometrical theory of conservative and non-conservative mechanical systems can be raised based on the Lagrangian and Hamiltonian geometries. And that these geometries relies on the mechanical principles. The book covers the following topics : Lagrange and Hamilton spaces  Lagrange and Hamilton spaces of higher order  Analytical Mechanics of Lagrangian and Hamiltonian mechanical systems. The novelty consists of the following:a geometrization of the classical non-conservative mechanical systems, whose external forces depend on velocities, the notion of Finslerian mechanical system, the definition of Cartan mechanical system, a theory of Lagrangian and Hamiltonian mechanical systems by means of the geometry of tangent (cotangent) bundle, the geometrization of the higher order Lagrangian and Hamiltonian mechanical systems, fundamental equations of Riemannian mechanical systems whose external forces depend on higher order accelerations.

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Tags: Applications geometries Hamiltonian Lagrangian Mechanics

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