1. Closed Elastic Curves and Rods
I: Euler’s Elastica

2. Acknowledgements Joel Langer, Case Western Reserve Univ.
Manuel Barros, Univ. of Granada, Spain
Oscar Garay, Univ. del Pais Vasco, Spain
Rongpei Huang, East China Normal Univ.
Thomas Ivey, College of Charleston, S.C.
Vel Jurdjevic, University of Toronto, Canada
Anders Linner, Northern Illinois Univ.
Daniel Steinberg, Dim Sum Thinking

3. Classical Bernoulli-Euler Elastica

4. Bending Energy Functionals

5. Deriving the Euler Equations

7. The Euler-Lagrange Equations

9. Use the Frenet Equations

11. Use Rotational Symmetry

13. Killing Fields

14. Conserved Quantities

16. Planar Elastic Curves

19. Cylindrical Coordinates

22. Non-planar elastic curves

23. A little bit of elliptic integrals

25. The Figure-Eight elastica

26. Finding Closed Curves

28. Closed Elastic Curves and Rods
II: Elastica in a Space Form

29. Riemannian Geometry

30. Curves in M

31. Some Useful Formulas

32. Proof of (3)

36. Euler-Lagrange Equations

38. Solutions

39. Killing Fields

41. Elastica on the 2-sphere

43. Wavelike elastic curves on the sphere

44. Classifying wavelike elastic curves on the sphere