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	<title>Melvin Leok's Professional Blog &#187; papers</title>
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	<link>http://intranet.math.purdue.edu/mleok</link>
	<description>Computational Geometric Mechanics and Control</description>
	<pubDate>Wed, 14 May 2008 20:58:15 +0000</pubDate>
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		<title>Preprint: Global Symplectic Uncertainty Propagation on SO(3)</title>
		<link>http://intranet.math.purdue.edu/mleok/2008/03/10/preprint-global-symplectic-uncertainty-propagation-on-so3/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2008/03/10/preprint-global-symplectic-uncertainty-propagation-on-so3/#comments</comments>
		<pubDate>Tue, 11 Mar 2008 03:01:44 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<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>
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		<title>Preprint: Time Optimal Attitude Control for a Rigid Body</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/09/19/preprint-time-optimal-attitude-control-for-a-rigid-body/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/09/19/preprint-time-optimal-attitude-control-for-a-rigid-body/#comments</comments>
		<pubDate>Wed, 19 Sep 2007 20:35:08 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<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>
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		<title>Preprint: Lagrangian Mechanics and Variational Integrators on Two-Spheres</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/07/02/preprint-lagrangian-mechanics-and-variational-integrators-on-two-spheres/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/07/02/preprint-lagrangian-mechanics-and-variational-integrators-on-two-spheres/#comments</comments>
		<pubDate>Mon, 02 Jul 2007 08:56:27 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<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>
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		<title>Preprint: Discrete Control Systems</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/05/29/preprint-discrete-control-systems/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/05/29/preprint-discrete-control-systems/#comments</comments>
		<pubDate>Tue, 29 May 2007 13:22:46 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<description><![CDATA[Invited article for the Springer Encyclopedia of Complexity and System Science
arxiv:0705.3868 [math.OC]
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that [...]]]></description>
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		<title>Preprint: Controlled Lagrangians and Stabilization of Discrete Mechanical Systems I</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/04/30/preprint-controlled-lagrangians-and-stabilization-of-discrete-mechanical-systems-i/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/04/30/preprint-controlled-lagrangians-and-stabilization-of-discrete-mechanical-systems-i/#comments</comments>
		<pubDate>Mon, 30 Apr 2007 05:21:06 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<description><![CDATA[Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the controlled Lagrangian approach in the discrete context that are not present in the continuous theory. In particular, to make the discrete theory effective, [...]]]></description>
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		<title>In press: Lie Group Variational Integrators for the Full Body Problem in Orbital Mechanics</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/04/30/in-press-lie-group-variational-integrators-for-the-full-body-problem-in-orbital-mechanics/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/04/30/in-press-lie-group-variational-integrators-for-the-full-body-problem-in-orbital-mechanics/#comments</comments>
		<pubDate>Mon, 30 Apr 2007 05:16:20 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<description><![CDATA[Celestial Mechanics and Dynamical Astronomy, 98(2), 121-144, 2007
Published online: 12 April 2007
doi:10.1007/s10569-007-9073-x
Equations of motion, referred to as full body models, are developed to describe the dynamics of rigid bodies acting under their mutual gravitational potential. Continuous equations of motion and discrete equations of motion are derived using Hamilton’s principle. These equations are expressed in an [...]]]></description>
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		</item>
		<item>
		<title>In press: Lie Group Variational Integrators for the Full Body Problem</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/04/30/in-press-lie-group-variational-integrators-for-the-full-body-problem/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/04/30/in-press-lie-group-variational-integrators-for-the-full-body-problem/#comments</comments>
		<pubDate>Mon, 30 Apr 2007 05:14:47 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
		<category><![CDATA[papers]]></category>

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		<description><![CDATA[Computer Methods in Applied Mechanics and Engineering, 196(29-30), 2907-2924, 2007
Available online: 7 March 2007
doi:10.1016/j.cma.2007.01.017
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of rigid body configurations. [...]]]></description>
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		<title>Preprint: A Combinatorial Optimal Control Problem for Spacecraft Formation Reconfiguration</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/02/24/preprint-a-combinatorial-optimal-control-problem-for-spacecraft-formation/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/02/24/preprint-a-combinatorial-optimal-control-problem-for-spacecraft-formation/#comments</comments>
		<pubDate>Sat, 24 Feb 2007 23:08:44 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
		<category><![CDATA[papers]]></category>

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		<description><![CDATA[We consider a spacecraft formation reconfiguration problem in the case of identical spacecraft. This introduces in the optimal reconfiguration problem a permutational degree of freedom, in addition to the choice of individual spacecraft trajectories. We approach this using a coupled combinatorial and continuous optimization framework, in which the inner loop consists of computing the costs [...]]]></description>
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		<title>Preprint: Propagation of Uncertainty in Rigid Body Attitude Flows</title>
		<link>http://intranet.math.purdue.edu/mleok/2007/02/24/preprint-propagation-of-uncertainty-in-rigid-body-attitude-flows/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2007/02/24/preprint-propagation-of-uncertainty-in-rigid-body-attitude-flows/#comments</comments>
		<pubDate>Sat, 24 Feb 2007 23:07:51 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<description><![CDATA[Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by Euler-Poincaré equations that describe the rotational dynamics of the rigid body acting under the influence of an attitude dependent potential and by [...]]]></description>
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		<title>Preprint: Optimal Attitude Control for a Rigid Body with Symmetry</title>
		<link>http://intranet.math.purdue.edu/mleok/2006/10/30/preprint-optimal-attitude-control-for-a-rigid-body-with-symmetry/</link>
		<comments>http://intranet.math.purdue.edu/mleok/2006/10/30/preprint-optimal-attitude-control-for-a-rigid-body-with-symmetry/#comments</comments>
		<pubDate>Tue, 31 Oct 2006 02:05:51 +0000</pubDate>
		<dc:creator>mleok</dc:creator>
		
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		<description><![CDATA[Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control moment that respects the symmetry. The symmetry in the attitude dynamics system yields a conserved quantity, and it causes [...]]]></description>
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