Idézet: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.

Idézet:? 1800616635.pdf (Miguel C Muñoz-Lecanda & Narciso Román-Roy) (2025) (9 MB)

Idézet:A kódrészlet megtekintéséhez be kell jelentkezned, vagy nincs jogosultságod a tartalom megtekintéséhez.

Idézet:A kódrészlet megtekintéséhez be kell jelentkezned, vagy nincs jogosultságod a tartalom megtekintéséhez.