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Global formulations of Lagrangian an...

Lee, Taeyoung.

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Global formulations of Lagrangian and Hamiltonian dynamics on manifolds = a geometric approach to modeling and analysis /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Global formulations of Lagrangian and Hamiltonian dynamics on manifolds/ by 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.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Lagrangian functions. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-56953-6
ISBN:	9783319569536

Global formulations of Lagrangian and Hamiltonian dynamics on manifolds = a 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

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

736400
Lagrangian functions.

LC Class. No.: QC20.7.C3

Dewey Class. No.: 515.39

Global formulations of Lagrangian and Hamiltonian dynamics on manifolds = a geometric approach to modeling and analysis /
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100 1 $a Lee, Taeyoung. $3 3295875
245 1 0 $a Global formulations of Lagrangian and Hamiltonian dynamics on manifolds $h [electronic resource] : $b a geometric approach to modeling and analysis / $c by Taeyoung Lee, Melvin Leok, N. Harris McClamroch.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xxvii, 539 p. : $b ill., digital ; $c 24 cm.
490 1 $a Interaction of mechanics and mathematics, $x 1860-6245
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.
650 0 $a Lagrangian functions. $3 736400
650 0 $a Hamiltonian systems. $3 629810
650 0 $a Manifolds (Mathematics) $3 612607
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Vibration, Dynamical Systems, Control. $3 893843
650 2 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
700 1 $a Leok, Melvin. $3 1934967
700 1 $a McClamroch, N. Harris. $3 3295876
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773 0 $t Springer eBooks
830 0 $a Interaction of mechanics and mathematics. $3 2059381
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-56953-6
950 $a Engineering (Springer-11647)