Rotation axis

Hey,

I'm trying to rotate and translate a mesh. But I want the mesh to move in z-direction in the rotated system and not in the inertia system. So I'm doing 3 rotations with

mesh_->rotate(totalPhix_,incrementalPhix,axisx_,reference_point);
vectorScalarMult3D(axisx_,omegax_,omegaVecx);
mesh_->rotate(totalPhiy_,incrementalPhiy,axisy_,reference_point);
vectorScalarMult3D(axisy_,omegay_,omegaVecy);
mesh_->rotate(totalPhiz_,incrementalPhiz,axisz_,reference_point);
vectorScalarMult3D(axisz_,omegaz_,omegaVecz);

and a linear movement in the rotated system in z with

vectorScalarMult3D(axisz_,vz,vel_[2]); // <-create a vector in z axis with length vz
// calculate total and incremental displacement
vectorScalarMult3D(vel_,dt,dx);
vectorAdd3D(dX_,dx,dX_);
// apply move
mesh_->move(dX_,dx);

The problem now is that the axisz_ vector is not rotated with the mesh. Therefor, I try to rotate the vector each step with

RotMatrix(incrementalPhix, incrementalPhiy, incrementalPhiz, Dnew_);
MatrixMultisMatrix(Dold_,Dnew_,Dold_); //matrix multiplication
MatrixMultisVector(Dold_, eyex_,axisx_); //matrix vector multiplication
MatrixMultisVector(Dold_, eyey_,axisy_);
MatrixMultisVector(Dold_, eyez_,axisz_);

where eye* is the unit vector in each direction. The RotMatrix is build up like in this paper for "kardan-winkel" (page 1 Matrix S)
http://www.itm.uni-stuttgart.de/courses/madyn/Merkblaetter/M08.pdf

the rotMatrix for 3 rotations is calculated on this way
D*D'*D''*eyez_
where D is the first rotation and D'' is the last.
But somehow the calculation of the rotated axis is wrong. Is there a function which I could use to rotate the axis with the mesh??

Thanks
Joshua