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			<div class="col-md-6 col-sm-12 col-xs-12"><h3><span >Classical Mechanics: A Computational Approach</span></h3></div>
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		<p style="margin:0;">We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.</p><br><p>We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincar&eacute; integral invariants; Poincar&eacute;-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion.</p><br><p>Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.</p>
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			<span class="grayedtext" style="text-decoration: line-through;">2008-09-01</span></div>	</td>
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