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. Read more... Abstract: 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

lgli/N:\!genesis_files_for_add\_add\Lee, Leok, McClamroch, Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 2018.epub

nexusstc/Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds/743a38c2285d45040196dddcf2346262.epub

scihub/10.1007/978-3-319-56953-6.pdf

Taeyoung Lee, Melvin Leok;McClamroch, N Harris

Lee, Taeyoung

Springer International Publishing : Imprint : Springer

Springer Nature Switzerland AG

Interaction of Mechanics and Mathematics - Springer, Cham, copyright 2018

Interaction of mechanics and mathematics series, Cham, Switzerland, 2018

Springer Nature (Textbooks & Major Reference Works), Cham, 2017

Interaction of mechanics and mathematics, Cham, 2017

Switzerland, Switzerland

1st ed. 2018, US, 2017

Aug 15, 2017

2, 20170814

lg2856203

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Source title: Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds: A Geometric Approach to Modeling and Analysis (Interaction of Mechanics and Mathematics)

2020-11-29