Elastic Energy - PDF Document

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  1. Elastic Energy Closed Elastic Curves and Closed Elastic Curves and Rods Rods III Kirchhoff Rods III Kirchhoff Rods Kirchhoff Elastic Rod The Darboux Vector Inertial Frames 1

  2. Torsion and Twisting 2

  3. Integrating the rod equations Closed Elastic Rods Closed Elastic Curves and Closed Elastic Curves and Rods Rods IV Hamiltonian systems IV Hamiltonian systems Geometric Hamiltonian Systems 3

  4. Poisson Brackets 4

  5. Lie Bracket Formulas Hamiltonians on E Symmetries simplify! 5

  6. Frenet Equations Example: The Kirchhoff Rod Pontrjagin Maximum Principle Liouville –Arnol’d Integrability 6

  7. End of Part 4 End of Part 4 More Examples ? 7