Titlebook: Analytical Mechanics; A Concise Textbook Sergio Cecotti Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusive lice

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Shuto Ogihara,Tomohiro Amemiya,Kazuma Aoyamae integrable by quadratures. Then we introduce the action-angle canonical variables which are illustrated in several examples. We define the adiabatic processes and their invariant and prove that the action variables are adiabatic invariants when the frequency of the associated angle is non-zero. We

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From Newtonian Dynamics to Lagrangian Mechanicse basic notions of ., ., and . We classify the possible kinds of constraints. Then we deduce the Lagrangian equations of motion using the d’Alembert principle of virtual works. We shall revisit these equations from higher standpoints in Chapters 3 and 4 after reviewing the required math tools in Cha

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Math Interlude: A Quick Review of Smooth Manifolds And All Thatacts and definitions of differential geometry mainly to fix notation and terminology. Topics reviewed: smooth manifolds, vector bundles, vector and tensor fields, differential forms and exterior algebra, Stokes theorem and applications, Lie derivative, Lie groups and algebras, Riemannian geometry an

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Lagrangian Mechanics on Manifoldsagrangian, its invariances in value and form, and we describe the most general force consistent with a Lagrangian formulation. In this context, we describe the mechanics of a particle moving in a general curved space-time in General Relativity. Most of the chapter is devoted to the relation between

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Lagrange Mechanics: Important Special Systems with one degree of freedom and show that they can always be solved by quadratures. In the case of bounded motion, we describe the functional relation between the shape of the potential and the period of the motion. Then we consider the two-body problem with a potential which depends only on the dis

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Symplectic Geometryout symplectic geometry including: Lagrangian submanifolds, symplectomorphisms and their generating functions, Darboux theorem, Poisson brackets, momentum maps, and the symplectic reduction with the Marsden–Weinstein–Meyer quotient. In the last section we introduce contact geometry and the related n

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