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federgraph-special-sample-maxima

federgraph Oct 17th, 2014 176 Never
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  1. /* federgraph-special-sample-maxima
  2.    see federgraph.blogspot.de
  3. */
  4.  
  5. kill(all)$
  6.  
  7. a1: (x-x1)^2 + (y-y1)^2$
  8. a2: (x-x2)^2 + (y-y2)^2$
  9. a3: (x-x3)^2 + (y-y3)^2$
  10.  
  11. t1: sqrt(a1)$
  12. t2: sqrt(a2)$
  13. t3: sqrt(a3)$
  14.  
  15. f1: (t1-l)$
  16. f2: (t2-l)$
  17. f3: (t3-l)$
  18.  
  19. u1: f1 * (x-x1) / t1$
  20. u2: f2 * (x-x2) / t2$
  21. u3: f3 * (x-x3) / t3$
  22.  
  23. v1: f1 * (y-y1) / t1$
  24. v2: f2 * (y-y2) / t2$
  25. v3: f3 * (y-y3) / t3$
  26.  
  27. u: u1 + u2 + u3$
  28. v: v1 + v2 + v3$
  29.  
  30. z: sqrt(u^2 + v^2);
  31.  
  32. /* equilateral triangle with side length a
  33.    h = height
  34.    ro = outer circle
  35.    ri = inner circle
  36. */
  37.  
  38. /* side length of triangle defined */
  39. a: 100$
  40.  
  41. h: sqrt(3)/2 * a$
  42. ri: sqrt(3)/3 * a$
  43. ro: sqrt(3)/6 * a$
  44.  
  45. /* constant triangle coordinates */
  46. x1: -ri$  
  47. x2: -ri$
  48. x3: ro$
  49. y1: -a/2$
  50. y2: a/2$
  51. y3: 0$
  52.  
  53. /* Parameter l is the original length of the springs.
  54.    All springs have the same original length.
  55.    We are exploring a special case where the minimum for z
  56.    touches the floor. It value of l is between 83 and 84.
  57.    But what is the exact value of l in terms of a?
  58.    ===============================================
  59.    And what is the x-value of the touchdown?
  60. */
  61. l: 83.5$
  62.  
  63. /* We examination of a cross section through surface. */
  64. y: 0$
  65.  
  66. /* The cross section  gives us a 2D plot for the special case. */
  67. plot2d(z, [x, -100, 100])$
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