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EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{α,β,γ},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@
  Dot[
    RotationMatrix[γ, {0, 0, -1}], 
    RotationMatrix[β, {-1, 0, 0}], 
    RotationMatrix[α, {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

 EulerMatrix[{α,β,γ},{3,2,3}]

or

 EulerMatrix[{α,β]β,γ}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@
  Dot[
   RotationMatrix[γ, {0, 0, -1}],
   RotationMatrix[β, {0, -1, 0}], 
   RotationMatrix[α, {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{α,β,γ},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@
  Dot[
    RotationMatrix[γ, {0, 0, -1}], 
    RotationMatrix[β, {-1, 0, 0}], 
    RotationMatrix[α, {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

 EulerMatrix[{α,β,γ},{3,2,3}]

or

 EulerMatrix[{α,β],γ}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@
  Dot[
   RotationMatrix[γ, {0, 0, -1}],
   RotationMatrix[β, {0, -1, 0}], 
   RotationMatrix[α, {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{α,β,γ},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@
  Dot[
    RotationMatrix[γ, {0, 0, -1}], 
    RotationMatrix[β, {-1, 0, 0}], 
    RotationMatrix[α, {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

 EulerMatrix[{α,β,γ},{3,2,3}]

or

 EulerMatrix[{α,β,γ}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@
  Dot[
   RotationMatrix[γ, {0, 0, -1}],
   RotationMatrix[β, {0, -1, 0}], 
   RotationMatrix[α, {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

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EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,1,3}]

EulerMatrix[{α,β,γ},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {-1, 0, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

Transpose@
  Dot[
    RotationMatrix[γ, {0, 0, -1}], 
    RotationMatrix[β, {-1, 0, 0}], 
    RotationMatrix[α, {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,2,3}]

 EulerMatrix[{α,β,γ},{3,2,3}]

or

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]}]

 EulerMatrix[{α,β],γ}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {0, -1, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

Transpose@
  Dot[
   RotationMatrix[γ, {0, 0, -1}],
   RotationMatrix[β, {0, -1, 0}], 
   RotationMatrix[α, {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {-1, 0, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,2,3}]

or

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {0, -1, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{α,β,γ},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@
  Dot[
    RotationMatrix[γ, {0, 0, -1}], 
    RotationMatrix[β, {-1, 0, 0}], 
    RotationMatrix[α, {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

 EulerMatrix[{α,β,γ},{3,2,3}]

or

 EulerMatrix[{α,β],γ}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@
  Dot[
   RotationMatrix[γ, {0, 0, -1}],
   RotationMatrix[β, {0, -1, 0}], 
   RotationMatrix[α, {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.

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source | link

EulerMatrix is available in MMA 10. To obtain the matrix for the transformation shown in your sketch, apply

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,1,3}]

This transformation is known as the x-convention, because the second rotation is about x'-axis. The Wikipedia designates this by ZXZ.

Those who do not have MMA 10 can obtain the same x-convention transformation using RotationMatrix applied 3 times. The code is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {-1, 0, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

As you know from the Wikipedia, there is more than one set of Euler angles. The y-convention is more common in quantum mechanics, so let me give that transformation here as well. In MMA 10, the y-convention transformation is

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]},{3,2,3}]

or

EulerMatrix[{\[Alpha],\[Beta],\[Gamma]}]

since the y-convention is the default when the axes are not specified. The Wikipedia designates this by ZYZ. In terms of the RotationMatrix function, the y-convention transformation is

Transpose@Dot[RotationMatrix[\[Gamma], {0, 0, -1}], RotationMatrix[\[Beta], {0, -1, 0}], RotationMatrix[\[Alpha], {0, 0, -1}]]

A reference for these transformations is Classical Mechanics by Herbert Goldstein, 2nd Edition, Section 4-4 and Appendix B.