Closed Elastic Curves and Rods

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Closed Elastic Curves and Rods

• III Kirchhoff Rods

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Kirchhoff Elastic Rod
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The Darboux Vector
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Elastic Energy
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Inertial Frames
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Torsion and Twisting
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Integrating the rod equations
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Closed Elastic Rods
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Closed Elastic Curves and Rods

• IV Hamiltonian systems

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Geometric Hamiltonian Systems
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Poisson Brackets
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Symmetries simplify!
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Lie Bracket Formulas
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Hamiltonians on E
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Frenet Equations
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Pontrjagin Maximum Principle
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Example The Kirchhoff Rod
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Liouville Arnold Integrability
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More Examples
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End of Part 4