SHARE
TWEET

Formulae

alseambusher Feb 18th, 2015 (edited) 37 Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
  1. \begin{bmatrix}
  2. hx&  hy& hz
  3. \end{bmatrix} =
  4. \begin{bmatrix}
  5. Ex&  Ey& Ez
  6. \end{bmatrix} *
  7. \begin{bmatrix}
  8. 0&  -g_{z}& g_{y}\\
  9. g_{z}&  0& -g_{x}\\
  10. -g_{y}&  g_{x}& 0
  11. \end{bmatrix}
  12. \\
  13. H = \begin{bmatrix}
  14. \frac{h_{x}}{| h\,|}
  15. &\frac{h_{y}}{| h\,|}
  16. & \frac{h_{z}}{| h\,|}
  17. \end{bmatrix}
  18. \\
  19. A = \begin{bmatrix}
  20. \frac{g_{x}}{| g\,|}
  21. &\frac{g_{y}}{| g\,|}
  22. & \frac{g_{z}}{| g\,|}
  23. \end{bmatrix}
  24. \\
  25.  
  26. \begin{bmatrix}
  27. Mx&  My& Mz
  28. \end{bmatrix} =
  29. \begin{bmatrix}
  30. Ax&  Ay& Az
  31. \end{bmatrix} *
  32. \begin{bmatrix}
  33. 0&  -H_{z}& H_{y}\\
  34. H_{z}&  0& -H_{x}\\
  35. -H_{y}&  H_{x}& 0
  36. \end{bmatrix}\\
  37. R=
  38. \begin{bmatrix}
  39. H_{x}&  H_{y}& H_{z}\\
  40. H_{x}&  H_{y}& H_{z}\\
  41. H_{x}&  H_{y}& H_{z}\\
  42. \end{bmatrix}\\
  43.  
  44. rates = Axis_{x}, Axis_{y} and \, Axis_{z}\\
  45.  
  46. time = dT\\
  47.  
  48. \omega = \sqrt{Axis^{2}_{x} + Axis^{2}_{y} +  Axis^{2}_{z}}\\
  49.  
  50. a = \begin{bmatrix}
  51. \frac{Axis_{x}}{| Axis\,|}
  52. &\frac{Axis_{y}}{| Axis\,|}
  53. & \frac{Axis_{z}}{| Axis\,|}
  54. \end{bmatrix}\\
  55.  
  56. \omega =\frac{d\theta }{dT} \Rightarrow d\theta = \omega dT
  57.  
  58. deltaRotationVector = \begin{bmatrix}
  59. a_{x} sin(\frac{d\theta}{2})&  a_{y} sin(\frac{d\theta}{2})& a_{z} sin(\frac{d\theta}{2}) & cos(\frac{d\theta}{2})
  60. \end{bmatrix}\\
  61.  
  62. rotationMatrix = rotationMatrix * deltaRotationMatrix = \begin{bmatrix}
  63. R_{1}&  R_{2}& R_{3} \\
  64. R_{4}&  R_{5}& R_{6} \\
  65. R_{7}&  R_{8}& R_{9}
  66. \end{bmatrix}\\
  67.  
  68. angles = \begin{bmatrix}
  69. tan^{-1}(\frac{R_{1}}{R_{4}})& sin^{-1}(R_{7}) &  tan^{-1}(\frac{R_{6}}{R_{8}})
  70. \end{bmatrix}\\
  71.  
  72. (X, Y) = (D*tan(angle_{x}), D*tan(angle_{y}))\\
RAW Paste Data
Top