Titlebook: Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds; A Geometric Approach Taeyoung Lee,Melvin Leok,N. Harris McClamroch

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https://doi.org/10.1007/978-3-663-05229-6The configuration manifold is a product of copies of the special orthogonal group . embedded in .. A Lagrangian function . is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several rotating rigid body systems are studied to illustrate the developments.

漸變

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Mathematical Background,A summary of the most important mathematical concepts used in the subsequent chapters is given. Differential geometric concepts of embedded manifolds, tangent vectors, and cotangent vectors are emphasized. Vector fields defined on embedded manifolds are introduced to characterize dynamic flows. The concepts are illustrated by examples.

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Lagrangian and Hamiltonian Dynamics on ,,The configuration manifold is a product of two-spheres embedded in .. A Lagrangian function . is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several mechanical systems are studied to illustrate the developments.

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Lagrangian and Hamiltonian Dynamics on ,,The configuration manifold is a product of copies of the special orthogonal group . embedded in .. A Lagrangian function . is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several rotating rigid body systems are studied to illustrate the developments.

adumbrate

Lagrangian and Hamiltonian Dynamics on ,,The configuration manifold is a product of copies of the special Euclidean group . embedded in .. A Lagrangian function . is introduced and variational methods are used to derive Euler–Lagrange equations and Hamilton’s equations. Several translating and rotating rigid body systems are studied to illustrate the developments.

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