Foundations of Computational Geometric Mechanics
<p>Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Computational algorithms obtained from a discrete Hamilton's principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserv...
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https://thesis.library.caltech.edu/831/1/01_thesis_double_sided_mleok.pdfhttps://thesis.library.caltech.edu/831/2/02_thesis_single_sided_mleok.pdf
https://thesis.library.caltech.edu/831/4/11_front_matter_mleok.pdf
https://thesis.library.caltech.edu/831/5/12_chapter_one_introduction_mleok.pdf
https://thesis.library.caltech.edu/831/6/13_chapter_two_discrete_routh_reduction_mleok.pdf
https://thesis.library.caltech.edu/831/7/14_chapter_three_discrete_exterior_calculus_mleok.pdf
https://thesis.library.caltech.edu/831/8/15_chapter_four_discrete_connections_mleok.pdf
https://thesis.library.caltech.edu/831/9/16_chapter_five_generalized_variational_integrators_mleok.pdf
https://thesis.library.caltech.edu/831/10/17_chapter_six_conclusions_mleok.pdf
https://thesis.library.caltech.edu/831/11/18_appendices_mleok.pdf
https://thesis.library.caltech.edu/831/12/19_back_matter_mleok.pdf
Leok, Melvin (2004) Foundations of Computational Geometric Mechanics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KDV0-WR34. https://resolver.caltech.edu/CaltechETD:etd-03022004-000251 <https://resolver.caltech.edu/CaltechETD:etd-03022004-000251>