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Global formulations of Lagrangian an...

Lee, Taeyoung.

Global formulations of Lagrangian and Hamiltonian dynamics on manifoldsa geometric approach to modeling and analysis /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Global formulations of Lagrangian and Hamiltonian dynamics on manifoldsby Taeyoung Lee, Melvin Leok, N. Harris McClamroch.
Reminder of title:	a geometric approach to modeling and analysis /
Author:	Lee, Taeyoung.
other author:	Leok, Melvin.
Published:	Cham :Springer International Publishing :2018.
Description:	xxvii, 539 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Lagrangian functions.
Online resource:	http://dx.doi.org/10.1007/978-3-319-56953-6
ISBN:	9783319569536$q(electronic bk.)

Global formulations of Lagrangian and Hamiltonian dynamics on manifoldsa geometric approach to modeling and analysis /
Lee, Taeyoung.

Global formulations of Lagrangian and Hamiltonian dynamics on manifoldsa geometric approach to modeling and analysis /[electronic resource] :by Taeyoung Lee, Melvin Leok, N. Harris McClamroch. - Cham :Springer International Publishing :2018. - xxvii, 539 p. :ill., digital ;24 cm. - Interaction of mechanics and mathematics,1860-6245. - Interaction of mechanics and mathematics..

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.

ISBN: 9783319569536$q(electronic bk.)

Standard No.: 10.1007/978-3-319-56953-6doiSubjects--Topical Terms:

229155
Lagrangian functions.

LC Class. No.: QC20.7.C3

Dewey Class. No.: 515.39

Global formulations of Lagrangian and Hamiltonian dynamics on manifoldsa geometric approach to modeling and analysis /
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505 0 $a 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.
520 $a 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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