3 deleted 1 character in body edited Nov 21 '15 at 20:22 LouisB 5,00911 gold badge77 silver badges1717 bronze badges 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. 2 deleted 22 characters in body edited Nov 21 '15 at 11:19 xyz 27033 gold badges2727 silver badges100100 bronze badges 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. 1 answered Nov 21 '15 at 11:11 LouisB 5,00911 gold badge77 silver badges1717 bronze badges 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.