Geometry Of Mechanics

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Narciso Roman-roy (Universitat Politecnica De Catalunya - Barcelonatech, Spain) Miguel C Munoz-lecanda (Universitat Politecnica De Catalunya - Barcelonatech, Spain)

Geometry Of Mechanics

Narciso Roman-roy (Universitat Politecnica De Catalunya - Barcelonatech, Spain), Miguel C Munoz-lecanda (Universitat Politecnica De Catalunya - Barcelonatech, Spain)

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English

World Scientific Europe Ltd
26 October 2025

Geometry; Mathematical physics

Series: Advanced Textbooks In Mathematics

Summary
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This book sets out to demonstrate, interpret, and analyse the geometrical structures underlying classical mechanics. Through exploring the applications of these structures in the context of dissipative, autonomous, and nonautonomous conservative dynamical systems, a series of insightful exercises are developed in order to both consolidate and clarify the theoretical concepts introduced.

Geometry of Mechanics provides an informative exploration of the classic geometrical structures, including the symplectic structure and its application for constructing Lagrangian and Hamiltonian formalisms of autonomous regular systems, the cosymplectic structure (and others) for nonautonomous (time-dependent) systems, and the Riemannian structure underlying systems of 'mechanical' type. Lesser-known frameworks are also investigated, such as the (Skinner-Rusk) unified Lagrangian-Hamiltonian formalism, a new geometric setting for the Hamilton-Jacobi equation, and the latest treatment of nonconservative systems by contact geometry. Although the main focus of this exposition is on the regular Lagrangian and Hamiltonian systems, singular systems are also briefly explained where applicable.

Each chapter concludes with a set of problems, some of which are intended to be solved solely by the application of results presented, while others contain instructive results complementary to those presented in the chapters, complete with comments, suggestions, and recommendations. Interested readers will also find an extensive and up-to-date bibliography, including a great number of works produced in recent decades related to all topics explored.

By: Narciso Roman-roy (Universitat Politecnica De Catalunya - Barcelonatech Spain), Miguel C Munoz-lecanda (Universitat Politecnica De Catalunya - Barcelonatech, Spain)
Imprint: World Scientific Europe Ltd
Country of Publication: United Kingdom
Volume: 0
ISBN: 9781800616639
ISBN 10: 1800616635
Series: Advanced Textbooks In Mathematics
Pages: 348
Publication Date: 26 October 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming