Generalized Serret-Andoyer Transformation and Applications for the Controlled Rigid Body
dc.contributor.author | Lum, Kai-Yew | en_US |
dc.contributor.author | Bloch, Anthony M. | en_US |
dc.date.accessioned | 2006-09-08T20:32:47Z | |
dc.date.available | 2006-09-08T20:32:47Z | |
dc.date.issued | 1999-03 | en_US |
dc.identifier.citation | Lum, Kai-Yew; Bloch, Anthony M.; (1999). "Generalized Serret-Andoyer Transformation and Applications for the Controlled Rigid Body." Dynamics and Control 9(1): 39-66. <http://hdl.handle.net/2027.42/42627> | en_US |
dc.identifier.issn | 0925-4668 | en_US |
dc.identifier.issn | 1573-8450 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42627 | |
dc.description.abstract | The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO (3) on T * SO (3)—a generalization and extension of Noether's theorem for Hamiltonian systems with symmetry. In fact, we go on to generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T * SO (3) with left-invariant, hyperregular Hamiltonian functions. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to the controlled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T * SO (3), the closed-loop motion of the main body can again be reduced to canonical form. This simplifies the stability proof for relative equilibria , which then amounts to verifying the classical Lagrange-Dirichlet criterion. Additionally, issues regarding numerical integration of closed-loop dynamics are also discussed. Part of this work has been presented in LumBloch:97a. | en_US |
dc.format.extent | 252596 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer Science+Business Media | en_US |
dc.subject.other | Engineering | en_US |
dc.subject.other | Engineering Design | en_US |
dc.subject.other | Hamiltonian System | en_US |
dc.subject.other | Canonical Transformation | en_US |
dc.subject.other | Group Symmetry | en_US |
dc.subject.other | Symplectic Form | en_US |
dc.subject.other | Symplectic Reduction | en_US |
dc.title | Generalized Serret-Andoyer Transformation and Applications for the Controlled Rigid Body | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mechanical Engineering | en_US |
dc.subject.hlbsecondlevel | Industrial and Operations Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, The University of Michigan, MI, 48109-1109 | en_US |
dc.contributor.affiliationother | DSO National Laboratories, 20 Science Park Drive, Singapore, 118230 | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42627/1/10638_2004_Article_187947.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1023/A:1008342708491 | en_US |
dc.identifier.source | Dynamics and Control | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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