| 1. | Both of these are much harder with matrices or Euler angles.
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| 2. | This is similar to the extrinsic rotation equivalence for Euler angles.
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| 3. | Euler angles can be defined by three of these rotations.
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| 4. | Sometimes, both kinds of sequences are called " Euler angles ".
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| 5. | Using it, the three Euler angles can be defined as follows:
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| 6. | Therefore, this matrix will be ( See Euler angles article ):
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| 7. | Euler angles are typically denoted as & psi;.
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| 8. | This allows us to simplify the definition of the Euler angles as follows:
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| 9. | Euler angles are also used extensively in the quantum mechanics of angular momentum.
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| 10. | Therefore, any discussion employing Euler angles should always be preceded by their definition.
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