MELVIN LEOK THESIS

Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure. Binary asteroids in the Near-Earth object population. These equations are expressed in an inertial frame and in relative coordinates. Cite article How to cite? The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space the cotangent bundle of shape space , in which the geometric phases have been removed.

Please log in below. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux’ theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure. Lie-Poisson integrator for rigid body dynamics in the solar system. This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry.

A Lie group variational integrator for the attitude dynamics of melvin leok thesis rigid body with applications to the 3D pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting melvin leok thesis structures in the reduced phase space the cotangent bundle of shape spacein which the geometric phases have been removed.

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Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double melvin leok thesis pendulum.

Lie group variational integrators for the full body problem in orbital mechanics | SpringerLink

Construction of high order symplectic integrators. By continuing to use this site you agree to our use of cookies. The following articles are merged in Scholar.

Lie group variational integrators for the full body problem in orbital melvin leok thesis.

Stability in the Full Two-Body problem. Efficient Lie-Poisson integrator for melvin leok thesis spin dynamics of rigid bodies. Computer Methods in Applied Mechanics and Engineering, Their combined citations are counted only for the first article.

Lie group variational integrators for the full body problem in orbital mechanics

Scheeres University of Colorado Verified email at colorado. Journal of Melvin leok thesis and Control Systems 15 3, This is a preview of subscription content, log in to check access. The discrete equations of motion, referred to as a Lie group variational integrator, provide a geometrically exact and numerically efficient computational method for simulating full body dynamics in orbital mechanics; they are symplectic and momentum preserving, and they exhibit good energy behavior for exponentially long melvin leok thesis periods.

Please log in below. To gain access to this content, please complete the Recommendation Form and we will follow up with your librarian or Institution on your behalf. Symmetry reduction of discrete Lagrangian mechanics on Lie groups. Decision and Control, and European Control Conference. Journal of Physics A: The Lie group variational integrator also preserves the melvin leok thesis structure without the use of local charts, reprojection, or constraints. Discrete versions of some melvin leok thesis integrable systems and factorization of matrix polynomials.

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Springer Google Scholar. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics.

Adrian Sandu Virginia Tech Verified email at vt. Articles 1—20 Show more.

Melvin Leok, Ph.D.

The system can’t perform the operation now. Backward analysis of numerical integrators and symplectic methods.

This “Cited by” count includes citations to the following articles in Scholar. Lie group variational integrators for the full body problem. In contrast, a traditional symplectic method melvin leok thesis canonical systems could require repeated coordinate changes if one is evoking Darboux’ theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost.

Geometric Numerical Integration, 2nd edn. Articles Cited by Co-authors. Our method melvin leok thesis still efficient as it can directly handle the essential non-canonical nature of the symplectic structure.

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