Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds [electronic resource] : A Geometric Approach to Modeling and Analysis / by Taeyoung Lee, Melvin Leok, N. Harris McClamroch.

Por: Lee, Taeyoung [author.]Colaborador(es): Leok, Melvin [author.] | McClamroch, N. Harris [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Interaction of Mechanics and MathematicsEditor: Cham : Springer International Publishing : Imprint: Springer, 2018Edición: 1st ed. 2018Descripción: XXVII, 539 p. 49 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783319569536Tema(s): Dynamics | Ergodic theory | Vibration | Dynamical systems | System theory | Computer mathematics | Dynamical Systems and Ergodic Theory | Vibration, Dynamical Systems, Control | Systems Theory, Control | Computational Mathematics and Numerical AnalysisFormatos físicos adicionales: Printed edition:: Sin título; Printed edition:: Sin títuloClasificación CDD: 515.39 | 515.48 Clasificación LoC:QA313Recursos en línea: Libro electrónicoTexto
Contenidos:
Mathematical Background -- Kinematics -- Classical Lagrangian and Hamiltonian Dynamics -- Langrangian and Hamiltonian Dynamics on (S1)n -- Lagrangian and Hamiltonian Dynamics on (S2)n -- Lagrangian and Hamiltonian Dynamics on SO(3) -- Lagrangian and Hamiltonian Dynamics on SE(3) -- Lagrangian and Hamiltonian Dynamics on Manifolds -- Rigid and Mult-body Systems -- Deformable Multi-body Systems -- Fundamental Lemmas of the Calculus of Variations -- Linearization as an Approximation to Lagrangian Dynamics on a Manifold.
En: Springer Nature eBookResumen: This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
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Acceso multiusuario

Mathematical Background -- Kinematics -- Classical Lagrangian and Hamiltonian Dynamics -- Langrangian and Hamiltonian Dynamics on (S1)n -- Lagrangian and Hamiltonian Dynamics on (S2)n -- Lagrangian and Hamiltonian Dynamics on SO(3) -- Lagrangian and Hamiltonian Dynamics on SE(3) -- Lagrangian and Hamiltonian Dynamics on Manifolds -- Rigid and Mult-body Systems -- Deformable Multi-body Systems -- Fundamental Lemmas of the Calculus of Variations -- Linearization as an Approximation to Lagrangian Dynamics on a Manifold.

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

UABC ; Temporal ; 01/01/2021-12/31/2023.

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