MELVIN LEOK THESIS

MELVIN LEOK THESIS

New citations to this author. Their combined citations are counted only for the first article. The following articles are merged in Scholar. Explicit expressions for Lie group, higher-order Euler-Poincar? We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics. Proceedings of the American Control Conference, , Journal of Physics A:

The system can’t perform the operation now. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar? International Journal for Numerical Methods in Engineering 79 9 , , Explicit expressions for Lie group, higher-order Euler-Poincar? Journal of Physics A: Articles 1—20 Show more. My profile My library Metrics Alerts.

Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques.

Foundations of computational geometric mechanics

Scheeres University of Colorado Verified email at colorado. New citations to this author. New articles by this author.

melvin leok thesis

Articles 1—20 Show more. International Journal for Numerical Methods in Engineering 79 9, Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature.

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Celestial Mechanics and Dynamical Astronomy 98 2, Journal of Dynamical and Control Systems 14 4, Citation Leok, Melvin Foundations of computational geometric mechanics. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar? Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing.

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Explicit expressions for Lie group, higher-order Euler-Poincar? Get my own profile Cited by View all All Since Citations h-index 27 19 iindex 61 Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex.

melvin leok thesis

New perspective on the U n Wigner-Racah calculus. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition that takes into account the principal bundle structure is introduced.

Melvin Leok, Ph.D.

In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as melvim of variational integrators. We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics.

melvin leok thesis

The following articles are merged in Scholar. Proceedings of the American Control Conference,leik Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics. Mathematical and General 20 14, My profile My library Metrics Alerts.

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No commercial reproduction, distribution, display or performance rights in this work are provided. Mathematical and General 39 19, New articles related to this author’s research. Computer Methods in Applied Mechanics and Engineering, This “Cited by” count includes citations to the following articles in Scholar. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute.

Their combined citations are counted only for the first article.

Foundations of computational geometric mechanics – CaltechTHESIS

Adrian Sandu Virginia Tech Verified email at vt. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. More information and software credits. Journal of Physics A: Journal of Dynamical and Control Systems 15 3,