Abstract
The configuration manifold is a product of copies of the special orthogonal group \(\mathsf{SO(3)}\) embedded in \(\mathbb{R}^{3\times 3}\). A Lagrangian function \(L: T(\mathsf{SO(3)} \times \ldots \times \mathsf{SO(3)}) \rightarrow \mathbb{R}^{1}\) 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.
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Lee, T., Leok, M., McClamroch, N.H. (2018). Lagrangian and Hamiltonian Dynamics on \(\mathsf{SO(3)}\) . In: Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds. Interaction of Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-56953-6_6
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DOI: https://doi.org/10.1007/978-3-319-56953-6_6
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