A01=Miguel C Munoz-lecanda
A01=Narciso Roman-roy
Actions of Lie Groups
and Newtonian Systems
and Riemannian Geometry
Author_Miguel C Munoz-lecanda
Author_Narciso Roman-roy
Category=PBM
Category=PHU
Conservation Laws
Conservative and Dissipative Systems
Contact
Cosymplectic
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eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Fiber Bundles
Hamiltonian
Lagrangian
Symmetries
Symplectic
Variational Principles
Product details
- ISBN 9781800616639
- Publication Date: 24 Oct 2025
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
