diff --git a/src/meshTools/coordinateSystems/coordinateRotation/coordinateRotation.H b/src/meshTools/coordinateSystems/coordinateRotation/coordinateRotation.H
index 41c88a3db1..ae91005e22 100644
--- a/src/meshTools/coordinateSystems/coordinateRotation/coordinateRotation.H
+++ b/src/meshTools/coordinateSystems/coordinateRotation/coordinateRotation.H
@@ -161,17 +161,20 @@ public:
             return true;
         }
 
+        //- Transform vector using transformation tensor
+        virtual vector transform(const vector& st) const = 0;
+
         //- Transform vectorField using transformation tensor field
         virtual tmp<vectorField> transform(const vectorField& st) const = 0;
 
-        //- Transform vector using transformation tensor
-        virtual vector transform(const vector& st) const = 0;
+        //- Inverse transform vector using transformation tensor
+        virtual vector invTransform(const vector& st) const = 0;
 
         //- Inverse transform vectorField using transformation tensor field
         virtual tmp<vectorField> invTransform(const vectorField& st) const = 0;
 
-        //- Inverse transform vector using transformation tensor
-        virtual vector invTransform(const vector& st) const = 0;
+        //- Transform tensor using transformation tensorField
+        virtual tensor transformTensor(const tensor& st) const = 0;
 
         //- Transform tensor field using transformation tensorField
         virtual tmp<tensorField> transformTensor
@@ -179,26 +182,22 @@ public:
             const tensorField& st
         ) const = 0;
 
-        //- Transform tensor using transformation tensorField
-        virtual tensor transformTensor(const tensor& st) const = 0;
+        //- Transform vector using transformation tensor and return
+        //  symmetrical tensor
+        virtual symmTensor transformVector(const vector& st) const = 0;
 
         //- Transform vectorField using transformation tensorField and return
-        // symmetrical tensorField
+        //  symmetrical tensorField
         virtual tmp<symmTensorField> transformVector
         (
             const vectorField& st
         ) const = 0;
 
-        //- Transform vector using transformation tensor and return
-        // symmetrical tensor
-        virtual symmTensor transformVector(const vector& st) const = 0;
-
 
     // Write
 
             //- Write
             virtual void write(Ostream&) const = 0;
-
 };
 
 
diff --git a/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.C b/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.C
index d79c49a9c9..bc71836ba1 100644
--- a/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.C
+++ b/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.C
@@ -40,20 +40,25 @@ namespace Foam
 
 // * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * * //
 
-Foam::tensor Foam::cylindrical::R(const vector& dir) const
+Foam::tensor Foam::cylindrical::R(const vector& p) const
 {
-    const vector e3 = e3_/mag(e3_);
-    const vector r = dir - (dir & e3)*e3;
+    vector dir = p - origin_;
+    dir /= mag(dir) + vSmall;
+
+    const vector axis = axis_/mag(axis_);
+    const vector r = dir - (dir & axis)*axis;
 
     if (mag(r) < small)
     {
         // If the point is on the axis choose any radial direction
-        return axesRotation(e3, perpendicular(e3)).R();
+        return axesRotation(axis, perpendicular(axis)).R();
     }
     else
     {
-        return axesRotation(e3, dir).R();
+        return axesRotation(axis, dir).R();
     }
+
+    return tensor(r, axis^r, axis);
 }
 
 
@@ -64,10 +69,7 @@ void Foam::cylindrical::init(const UList<vector>& points)
 
     forAll(points, i)
     {
-        vector dir = points[i] - origin_;
-        dir /= mag(dir) + vSmall;
-
-        R[i] = this->R(dir);
+        R[i] = this->R(points[i]);
     }
 }
 
@@ -83,7 +85,7 @@ Foam::cylindrical::cylindrical
 :
     Rptr_(),
     origin_(origin),
-    e3_(axis)
+    axis_(axis)
 {
     init(points);
 }
@@ -92,17 +94,19 @@ Foam::cylindrical::cylindrical
 Foam::cylindrical::cylindrical(const dictionary& dict)
 :
     Rptr_(),
-    origin_(),
-    e3_()
+    origin_
+    (
+        dict.parent().found("origin")
+      ? dict.parent().lookup("origin")
+      : dict.lookup("origin")
+    ),
+    axis_
+    (
+        dict.found("e3")
+      ? dict.lookup("e3")
+      : dict.lookup("axis")
+    )
 {
-    // If origin is specified in the coordinateSystem
-    if (dict.parent().found("origin"))
-    {
-        dict.parent().lookup("origin") >> origin_;
-    }
-
-    // Rotation axis
-    dict.lookup("e3") >> e3_;
 }
 
 
@@ -135,10 +139,7 @@ void Foam::cylindrical::updatePoints(const UList<vector>& points)
 
     forAll(points, i)
     {
-        vector dir = points[i] - origin_;
-        dir /= mag(dir) + vSmall;
-
-        R[i] = this->R(dir);
+        R[i] = this->R(points[i]);
     }
 }
 
@@ -270,7 +271,7 @@ Foam::symmTensor Foam::cylindrical::transformVector
 
 void Foam::cylindrical::write(Ostream& os) const
 {
-     writeEntry(os, "e3", e3());
+     writeEntry(os, "axis", axis());
 }
 
 
diff --git a/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.H b/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.H
index 91ce59a0bc..695d90f51b 100644
--- a/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.H
+++ b/src/meshTools/coordinateSystems/coordinateRotation/cylindrical.H
@@ -28,15 +28,15 @@ Description
     A local coordinate rotation.
 
     The rotational field can be created in two ways:
-      -# Each rotational tensor is defined with two vectors (\c dir and \c e3)
-         where <tt>dir = point - origin</tt> and \c e3 is the rotation axis.
+      -# Each rotational tensor is defined with two vectors (\c dir and \c axis)
+         where <tt>dir = point - origin</tt> and \c axis is the rotation axis.
           Per each point an axesRotation type of rotation is created
           (cylindrical coordinates). For example:
           \verbatim
           cylindrical
           {
               type        localAxes;
-              e3          (0 0 1);
+              axis          (0 0 1);
           }
           \endverbatim
 
@@ -76,14 +76,14 @@ class cylindrical
         point origin_;
 
         //- Rotation axis
-        vector e3_;
+        vector axis_;
 
 
     // Private members
 
         //- Return the local transformation tensor
-        //  corresponding to the given vector
-        tensor R(const vector& dir) const;
+        //  corresponding to the given point
+        tensor R(const vector& p) const;
 
         //- Initialise transformation tensor field for given points
         void init(const UList<vector>& points);
@@ -151,26 +151,14 @@ public:
         //- Return local Cartesian z-axis in global coordinates
         virtual const vector e3() const
         {
-            return e3_;
+            return axis_;
         }
 
-        //- Transform vectorField using transformation tensor field
-        virtual tmp<vectorField> transform(const vectorField& tf) const;
-
-        //- Transform vector using transformation tensor
-        virtual vector transform(const vector& v) const;
-
-        //- Transform vector using transformation tensor for component
-        virtual vector transform(const vector& v, const label cmptI) const;
-
-        //- Inverse transform vectorField using transformation tensor field
-        virtual tmp<vectorField> invTransform(const vectorField& vf) const;
-
-        //- Inverse transform vector using transformation tensor
-        virtual vector invTransform(const vector& v) const;
-
-        //- Inverse transform vector using transformation tensor for component
-        virtual vector invTransform(const vector& v, const label cmptI) const;
+        //- Return local Cartesian z-axis in global coordinates
+        virtual const vector axis() const
+        {
+            return axis_;
+        }
 
         //- Return if the rotation is uniform
         virtual bool uniform() const
@@ -178,23 +166,41 @@ public:
             return false;
         }
 
-        //- Transform tensor field using transformation tensorField
-        virtual tmp<tensorField> transformTensor(const tensorField& tf) const;
+        //- Transform vector using transformation tensor
+        virtual vector transform(const vector& v) const;
+
+        //- Transform vectorField using transformation tensor field
+        virtual tmp<vectorField> transform(const vectorField& tf) const;
+
+        //- Transform vector using transformation tensor for component
+        virtual vector transform(const vector& v, const label cmptI) const;
+
+        //- Inverse transform vector using transformation tensor
+        virtual vector invTransform(const vector& v) const;
+
+        //- Inverse transform vectorField using transformation tensor field
+        virtual tmp<vectorField> invTransform(const vectorField& vf) const;
+
+        //- Inverse transform vector using transformation tensor for component
+        virtual vector invTransform(const vector& v, const label cmptI) const;
 
         //- Transform tensor using transformation tensorField
         virtual tensor transformTensor(const tensor& t) const;
 
+        //- Transform tensor field using transformation tensorField
+        virtual tmp<tensorField> transformTensor(const tensorField& tf) const;
+
+        //- Transform vector using transformation tensor and return
+        //  symmetrical tensor
+        virtual symmTensor transformVector(const vector& v) const;
+
         //- Transform vectorField using transformation tensorField and return
-        // symmetrical tensorField
+        //  symmetrical tensorField
         virtual tmp<symmTensorField> transformVector
         (
             const vectorField& vf
         ) const;
 
-        //- Transform vector using transformation tensor and return
-        // symmetrical tensor (R & st & R.T())
-        virtual symmTensor transformVector(const vector& v) const;
-
 
     // Write