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Closed Elastic Curves and Rods

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Presentation on theme: "Closed Elastic Curves and Rods"— Presentation transcript:

1 Closed Elastic Curves and Rods
III Kirchhoff Rods

2 Kirchhoff Elastic Rod

3 The Darboux Vector

4 Elastic Energy

5

6 Inertial Frames

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9 Torsion and Twisting

10

11

12 Integrating the rod equations

13 Closed Elastic Rods

14

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16 Closed Elastic Curves and Rods
IV Hamiltonian systems

17 Geometric Hamiltonian Systems

18 Poisson Brackets

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26 Symmetries simplify!

27 Lie Bracket Formulas

28 Hamiltonians on E

29

30 Frenet Equations

31

32 Pontrjagin Maximum Principle

33

34 Example: The Kirchhoff Rod

35 Liouville –Arnol’d Integrability

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37 More Examples

38 ?

39 End of Part 4


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