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	<title>Melvin Leok's Professional Blog</title>
	<link>http://intranet.math.purdue.edu/mleok</link>
	<description>Computational Geometric Mechanics and Control</description>
	<lastBuildDate>Wed, 14 May 2008 20:58:15 +0000</lastBuildDate>
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		<title>Taeyoung Lee successfully defended his PhD thesis on May 8, 2008</title>
		<description><![CDATA[My first PhD student, Taeyoung Lee, successfully defended his PhD thesis entitled, &#8220;Computational Geometric Mechanics and Control of Rigid Bodies,&#8221; on May 8, 2008.
He was jointly co-advised by Prof. N. Harris McClamroch. The other members of the doctoral committee were Prof. Anthony Bloch, Prof. Jessy Grizzle, and Prof. Daniel Scheeres.
Amongst Taeyoung&#8217;s many honors, he recently [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2008/05/13/taeyoung-lee-successfully-defended-his-phd-thesis-on-may-8-2008/</link>
			</item>
	<item>
		<title>New additions to Computational Geometric Mechanics @ Purdue</title>
		<description><![CDATA[
Diana Sosa Mart&#237;n, who recently received her PhD in Mathematics from the University of La Laguna in Spain, will be joining Purdue University as a visiting assistant professor for the 2008/2009 academic year. Her research interests include geometric mechanics on Lie groupoids and algebroids.
Tomoki Ohsawa, a mathematics graduate student at the University of Michigan, will [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2008/05/13/diana-sosa-martin-joining-purdue-as-a-visiting-assistant-professor/</link>
			</item>
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		<title>Preprint: Global Symplectic Uncertainty Propagation on SO(3)</title>
		<description><![CDATA[[&#160;PDF&#160;&#124;&#160;arXiv:0803.1515 [math.DS]&#160;]
This paper introduces a global uncertainty propagation scheme for rigid body dynamics, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method is distinguished from prior approaches, as it allows one to consider probability densities that are global, and are not supported on only a single coordinate [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2008/03/10/preprint-global-symplectic-uncertainty-propagation-on-so3/</link>
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		<title>NSF CAREER Award DMS-0747659</title>
		<description><![CDATA[I have received a National Science Foundation Faculty Early Career Development (CAREER) Award in support of my work on &#8220;Computational Geometric Mechanics: Foundations, Computation, and Applications.&#8221; This is being funded by the Applied Mathematics Program of the Division of Mathematical Sciences.
NSF DMS-0747659
CAREER: Computational Geometric Mechanics: Foundations, Computation, and Applications
Melvin Leok, Purdue University
Abstract:
Symmetry, and the study [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2008/01/23/nsf-career-award/</link>
			</item>
	<item>
		<title>Postdoctoral, Graduate, and Undergraduate Positions Available</title>
		<description><![CDATA[Research positions for postdoctoral scholars, graduate students, and undergraduates are available in the broad area of geometric numerical methods in geometric mechanics and control. A description of my current research may be found in my research statement and my bibliography.
These positions are funded in part by research grants from the National Science Foundation in Applied [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/12/05/postdoctoral-graduate-and-undergraduate-positions-available/</link>
			</item>
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		<title>Pizza lunchtime seminar on Friday, November 16, 2007</title>
		<description><![CDATA[I will be giving a seminar during the Applied Mathematics pizza lunchtime seminar on Friday, November 16, 2007, from 11:30am to 12:15pm in REC 122. It will be geared towards first and second year graduate students. The title and abstract follows:
Lie Group and Homogeneous Variational Integrators and their Applications to Geometric Optimal Control Theory
Melvin Leok
The [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/11/13/pizza-lunchtime-seminar-on-friday-november-16-2007/</link>
			</item>
	<item>
		<title>Course Announcement: MATH 692 Geometric Numerical Integration</title>
		<description><![CDATA[I will be offering a graduate special topics course on geometric numerical integration in Spring 2008. Students who are interested are strongly encouraged to preregister for the course before the registration deadline of November 1, 2007, in order to ensure that the course has sufficient enrollment to be offered.
Course Description
MATH 692: Geometric Numerical Integration
Spring 2008, [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/10/22/course-announcement-math-692-geometric-numerical-integration/</link>
			</item>
	<item>
		<title>Preprint: Time Optimal Attitude Control for a Rigid Body</title>
		<description><![CDATA[[ PDF &#124; arXiv:0709.2514 [math.OC] ]
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control input. Necessary conditions for optimality are developed directly on the special orthogonal group [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/09/19/preprint-time-optimal-attitude-control-for-a-rigid-body/</link>
			</item>
	<item>
		<title>NSF Computational Mathematics LTB Grant</title>
		<description><![CDATA[I was awarded a NSF Computational Mathematics grant as part of the focused topic area on Long Time Behavior (LTB) of Numerical Methods in Large Scale Scientific Computing. It is entitled Generalized Variational Integators for Large-Scale Scientific Computation, and involves combining variational integrator methods from geometric integration with techniques from numerical analysis, approximation theory, and [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/08/24/nsf-computational-mathematics-ltb-grant/</link>
			</item>
	<item>
		<title>Preprint: Lagrangian Mechanics and Variational Integrators on Two-Spheres</title>
		<description><![CDATA[[ PDF &#124; arXiv:0707.0022 [math.NA] ]
Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global equations of motion. Both  continuous equations of motion and variational integrators completely avoid the singularities and [...]]]></description>
		<link>http://intranet.math.purdue.edu/mleok/2007/07/02/preprint-lagrangian-mechanics-and-variational-integrators-on-two-spheres/</link>
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