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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 6: Continue reading Chapter 3 Further development of the “calculus of variation”. Brachistochrone problem: (solved by Newton in 1696)

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. PHY 711 Classical Mechanics and Mathematical Methods • 10-10:50 AM MWF Olin 103 • Plan for Lecture 6: • Continue reading Chapter 3 • Further development of the “calculus of variation” PHY 711 Fall 2013 -- Lecture 6

  2. PHY 711 Fall 2013 -- Lecture 6

  3. Brachistochrone problem: (solved by Newton in 1696) http://mathworld.wolfram.com/BrachistochroneProblem.html A particle of weight mg travels frictionlessly down a path of shape y(x). What is the shape of the path y(x) that minimizes the travel time from y(0)=0 to y(p)=-2 ? PHY 711 Fall 2013 -- Lecture 6

  4. PHY 711 Fall 2013 -- Lecture 6

  5. PHY 711 Fall 2013 -- Lecture 6

  6. Parametric equations for Brachistochrone: PHY 711 Fall 2013 -- Lecture 6

  7. Brachistochrone problem -- summary Parametric equations; PHY 711 Fall 2013 -- Lecture 6

  8. Brachistochrone problem -- summary PHY 711 Fall 2013 -- Lecture 6

  9. Shape of a rope of length L and mass density r hanging between two points x1 y1 x2 y2 PHY 711 Fall 2013 -- Lecture 6

  10. Lagrange multiplier PHY 711 Fall 2013 -- Lecture 6

  11. PHY 711 Fall 2013 -- Lecture 6

  12. PHY 711 Fall 2013 -- Lecture 6

  13. PHY 711 Fall 2013 -- Lecture 6

  14. Summary of results PHY 711 Fall 2013 -- Lecture 6

  15. Application to particle dynamics PHY 711 Fall 2013 -- Lecture 6

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