Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds A Geometric Approach to Modeling and Analysis /

• Main Authors: Lee, Taeyoung (Author, http://id.loc.gov/vocabulary/relators/aut), Leok, Melvin (http://id.loc.gov/vocabulary/relators/aut), McClamroch, N. Harris (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Interaction of Mechanics and Mathematics,
• Subjects: 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 Analysis.

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 th...

Table of Contents:

• 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.