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# Formulae

alseambusher Feb 18th, 2015 (edited) 41 Never
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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}))\\
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