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Euler’s Elastica

Euler’s Elastica. v/ Steen Markvorsen. L. Euler (1707-1783). H. C. Ørsted (1777-1851) in persona. Ørsted (1999 - ) in space. Ørsted’s bom. Euler’s differentialligning. C. Hyughens (1629-1695). De er ens!. De har derfor de samme løsninger!.

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Euler’s Elastica

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  1. Euler’s Elastica v/ Steen Markvorsen

  2. L. Euler (1707-1783)

  3. H. C. Ørsted (1777-1851)in persona

  4. Ørsted (1999 - )in space

  5. Ørsted’s bom

  6. Euler’s differentialligning

  7. C. Hyughens (1629-1695)

  8. De er ens!

  9. De har derfor de samme løsninger! Hvis de altså har samme begyndelsesbetinger

  10. De har derfor de samme løsninger Hvis de altså har samme begyndelsesbetinger

  11. De har derfor de samme løsninger Hvis de altså har samme begyndelsesbetinger

  12. De har derfor de samme løsninger Hvis de altså har samme begyndelsesbetingelser

  13. Den fundne elastiske kurve

  14. D. Bernoulli (1700-1782) Lemniscaten

  15. Sammenligning

  16. Sammenligning, zoom De to kurver er tilsyneladende forskellige

  17. Euler’s Elastica Øvelser vedr. den fælles differentialligning • Linearisér, find, og vis løsningerne for små start-vinkler. • Find udtryk for de eksakte løsninger. • Find udtrykket for energien i pendulet som funktion af begyndelsesbetingelserne. • Find det algebraiske udtryk for Bernouilli’s lemniscat. • Vis, at de to kurver ikke er ens.

  18. Euler’s Elastica Referencer • www.mat.dtu.dk/people/S.Markvorsen/DISPLAY/Euler/

  19. Euler’s ElasticaSlut

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