We demonstrate in this notebook how the Euler angle conventions can be set for RotationMatrix3D[] and Rotate3D[].

<< Geometry`Rotations`

We also load other needed packages:

<< Graphics`Polyhedra`

<< Graphics`Shapes`

?RotationMatrix3D

?AngleConvention

x-convention (default)

?XConvention

SetOptions[RotationMatrix3D, 
        AngleConvention -> XConvention];

Do[
        Show[GraphicsArray[{RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], u, 0, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, u, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, 0, u]}]], {u, 
          0, π/2 - π/30, π/30}];

y-convention

?YConvention

SetOptions[RotationMatrix3D, 
        AngleConvention -> YConvention];

Do[
        Show[GraphicsArray[{RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], u, 0, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, u, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, 0, u]}]], {u, 
          0, π/2 - π/30, π/30}];

xyz-convention (pitch/roll/yaw)

?XYZConvention

SetOptions[RotationMatrix3D, 
        AngleConvention -> XYZConvention];

Do[
        Show[GraphicsArray[{RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], u, 0, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, u, 0], 
              RotateShape[
                Polyhedron[Cube, Boxed -> False, 
                  PlotRange -> {{-1.5, 1.5}, {-1.5, 
                        1.5}, {-1.5, 1.5}}], 0, 0, u]}]], {u, 
          0, π/2 - π/30, π/30}];