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Closed Elastic Curves and Rods

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.

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Closed Elastic Curves and Rods

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  1. Closed Elastic Curves and Rods III Kirchhoff Rods

  2. Kirchhoff Elastic Rod

  3. The Darboux Vector

  4. Elastic Energy

  5. Inertial Frames

  6. Torsion and Twisting

  7. Integrating the rod equations

  8. Closed Elastic Rods

  9. Closed Elastic Curves and Rods IV Hamiltonian systems

  10. Geometric Hamiltonian Systems

  11. Poisson Brackets

  12. Symmetries simplify!

  13. Lie Bracket Formulas

  14. Hamiltonians on E

  15. Frenet Equations

  16. Pontrjagin Maximum Principle

  17. Example: The Kirchhoff Rod

  18. Liouville –Arnol’d Integrability

  19. More Examples

  20. ?

  21. End of Part 4

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