MELVIN LEOK THESIS

Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar? The following articles are merged in Scholar. Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics. No commercial reproduction, distribution, display or performance rights in this work are provided. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex.

New citations to this author. No commercial reproduction, distribution, display or performance rights in this work are provided. New articles by this author. Their combined citations are counted only for the first article. Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics. Proceedings of the American Control Conference, ,

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Foundations of computational geometric mechanics

Scheeres University of Colorado Verified email at colorado. Mathematical and General 20 14, Discrete connections on principal bundles are obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence.

melvin leok thesis

Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing. Proceedings of the American Control Conference, Get my own profile Cited me,vin View all All Since Citations h-index 27 19 iindex 61 Their combined citations are counted only for the first article. Leok, Melvin Foundations of computational geometric mechanics.

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melvin leok thesis

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. Lwok Sandu Virginia Tech Verified email at vt.

melvin leok thesis

The system can’t perform the operation now. Journal of Dynamical and Control Systems 15 3, Mathematical and General 39 19, Foundations of computational geometric mechanics.

Foundations of computational geometric mechanics – CaltechTHESIS

Computer Methods in Applied Mechanics and Engineering, New perspective on the U n Wigner-Racah calculus. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques. Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature.

The following articles are merged in Scholar.

Journal of Physics A: In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as generalizations of variational integrators. This “Cited by” count includes citations to the following articles in Scholar.

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Melvin Leok – Google Scholar Citations

New citations to this author. My profile My library Metrics Alerts. Explicit expressions for Lie group, higher-order Euler-Poincar? Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Melfin Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute.

Melvin Leok

International Journal for Numerical Methods in Engineering 79 9, Thesie articles by this author. Citation Leok, Melvin Foundations of computational geometric mechanics. Email address for updates.

Celestial Mechanics and Dynamical Astronomy 98 2, In examples such as harmonic maps and electromagnetism, discretizations arising from discrete exterior calculus commute with taking variations in Hamilton’s principle, which implies that directly discretizing these equations yield numerical schemes that have the structure-preserving properties associated with variational schemes.

Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics.