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Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Celestial Mechanics and Dynamical Astronomy 98 2 , , Email address for updates. Mathematical and General 20 14 , , More information and software credits. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Journal of Physics A:

Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute. Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics. Discrete connections on principal bundles are obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence. Leok, Melvin Foundations of computational geometric mechanics. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques.

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

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Proceedings of the American Control Conference,nelvin 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. Their combined citations are counted only for the first article.

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New perspective on the U n Wigner-Racah calculus. Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Leok, Melvin Foundations of computational geometric mechanics.

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melvin leok thesis

Journal of Dynamical and Control Systems 15 3, Journal of Leook and Control Systems 14 4, Adrian Sandu Virginia Tech Verified email at vt. Abstract Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques.

Melvin Leok, Ph.D.

Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing. New citations to this author. In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. International Journal for Numerical Methods in Engineering 79 9, 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.

Mathematical and General 39 19, Computer Methods in Applied Mechanics and Engineering, New articles by this author. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. The following articles are merged in Scholar.

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Foundations of computational geometric mechanics

New articles related to this author’s research. Get my own profile Cited by View all All Since Citations h-index 27 19 iindex 61 Foundations of computational geometric mechanics. Journal of Physics A: Email address for updates. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar?

Mathematical and General 20 14, Articles 1—20 Show more.

melvin leok thesis

We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics.

Scheeres University of Colorado Verified email at colorado. The system can’t perform the operation now. Foundations of computational geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics.

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. A Caltech Library Service.