MELVIN LEOK THESIS

In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. Get my own profile Cited by View all All Since Citations h-index 27 19 iindex 61 Abstract Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Articles 1—20 Show more. Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques.

International Journal for Numerical Methods in Engineering 79 9 , , Proceedings of the American Control Conference, , Mathematical and General 39 19 , , Citation Leok, Melvin Foundations of computational geometric mechanics. Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques.

melvin leok thesis

Mathematical and General 20 14, In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as generalizations of variational integrators. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute.

Email address for updates. Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Abstract Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Discrete notions of differential forms, exterior derivatives, Hodge stars, codifferentials, sharps, flats, wedge products, contraction, Lie derivative, and the Poincar?

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Journal of Dynamical and Control Systems 14 4, The following articles are merged in Scholar.

Articles Cited by Co-authors. Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Adrian Sandu Virginia Tech Verified email at vt. Discrete Routh reduction is developed for abelian symmetries, and extended to systems with constraints and forcing.

New perspective on the U thess Wigner-Racah calculus.

Foundations of computational geometric mechanics

Computational algorithms obtained from a discrete Hamilton’s principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserving properties that can be ascribed to their variational derivation. Citation Leok, Melvin Foundations of computational geometric mechanics. More information and software credits. 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.

This “Cited by” count includes citations to the following articles in Scholar. Proceedings of the American Control Conference, New articles related to this author’s research. Computer Methods in Applied Mechanics and Engineering, The system can’t perform the operation now.

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New articles by this author. 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. Leok, Melvin Foundations of computational geometric mechanics.

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

Foundations of computational geometric mechanics – CaltechTHESIS

Articles 1—20 Show more. Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Discrete connections on principal bundles yhesis obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence.

Journal of Dynamical and Control Systems 15 3, Explicit expressions for Lie group, higher-order Euler-Poincar? A Caltech Library Service. New citations to this author.

Mathematical and General 39 19, International Journal for Numerical Methods in Engineering 79 9,

melvin leok thesis