Closed Elastic Curves and Rods

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Presentation transcript:

Closed Elastic Curves and Rods III Kirchhoff Rods

Kirchhoff Elastic Rod

The Darboux Vector

Elastic Energy

Inertial Frames

Torsion and Twisting

Integrating the rod equations

Closed Elastic Rods

Closed Elastic Curves and Rods IV Hamiltonian systems

Geometric Hamiltonian Systems

Poisson Brackets

Symmetries simplify!

Lie Bracket Formulas

Hamiltonians on E

Frenet Equations

Pontrjagin Maximum Principle

Example: The Kirchhoff Rod

Liouville –Arnol’d Integrability

More Examples

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End of Part 4