| 21. | The formulas in that section use different conventions for the Euler angles within that same section.
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| 22. | Gun orders include angles computed from the vertical gyro data, and those computations involve Euler angles.
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| 23. | This is also true for representations based on sequences of three Euler angles ( see below ).
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| 24. | So that gives you a lower bound on number of spindles, the Euler angles may do you.
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| 25. | However, the definition of Euler angles is not unique and in the literature many different conventions are used.
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| 26. | Therefore, gyros are used to know the actual orientation of moving spacecraft, and Euler angles are directly measurable.
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| 27. | Different authors may use different sets of rotation axes to define Euler angles, or different names for the same angles.
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| 28. | Thus " Euler angles are not vectors ", despite a similarity in appearance as a triple of numbers.
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| 29. | These singularities are not characteristic of the rotation matrix as such, and only occur with the usage of Euler angles.
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| 30. | Then, the transformation from the,, coordinate frame to the,, frame with the Euler angles,, is:
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