LEADER 04766nam 22007215 450 001 9910299917403321 005 20200704115044.0 010 $a3-319-56953-8 024 7 $a10.1007/978-3-319-56953-6 035 $a(CKB)3710000001630954 035 $a(DE-He213)978-3-319-56953-6 035 $a(MiAaPQ)EBC6311944 035 $a(MiAaPQ)EBC5596370 035 $a(Au-PeEL)EBL5596370 035 $a(OCoLC)1076233203 035 $a(PPN)203850963 035 $a(EXLCZ)993710000001630954 100 $a20170814d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGlobal Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds $eA Geometric Approach to Modeling and Analysis /$fby Taeyoung Lee, Melvin Leok, N. Harris McClamroch 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXVII, 539 p. 49 illus.) 225 1 $aInteraction of Mechanics and Mathematics,$x1860-6245 311 $a3-319-56951-1 327 $aMathematical 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. 330 $aThis book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics. 410 0$aInteraction of Mechanics and Mathematics,$x1860-6245 606 $aDynamics 606 $aErgodic theory 606 $aVibration 606 $aDynamical systems 606 $aSystem theory 606 $aComputer mathematics 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aVibration. 615 0$aDynamical systems. 615 0$aSystem theory. 615 0$aComputer mathematics. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aVibration, Dynamical Systems, Control. 615 24$aSystems Theory, Control. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a530.15564 700 $aLee$b Taeyoung$4aut$4http://id.loc.gov/vocabulary/relators/aut$01061150 702 $aLeok$b Melvin$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMcClamroch$b N. Harris$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299917403321 996 $aGlobal Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds$92517686 997 $aUNINA