# crv2rotation¶

Given a Cartesian rotation vector, $$\boldsymbol{\Psi}$$, the function produces the rotation matrix required to rotate a vector according to $$\boldsymbol{\Psi}$$.

The rotation matrix is given by

$\mathbf{R} = \mathbf{I} + \frac{\sin||\boldsymbol{\Psi}||}{||\boldsymbol{\Psi}||} \tilde{\boldsymbol{\Psi}} + \frac{1-\cos{||\boldsymbol{\Psi}||}}{||\boldsymbol{\Psi}||^2}\tilde{\boldsymbol{\Psi}} \tilde{\boldsymbol{\Psi}}$

To avoid the singularity when $$||\boldsymbol{\Psi}||=0$$, the series expansion is used

$\mathbf{R} = \mathbf{I} + \tilde{\boldsymbol{\Psi}} + \frac{1}{2!}\tilde{\boldsymbol{\Psi}}^2.$
param psi

Cartesian rotation vector $$\boldsymbol{\Psi}$$.

type psi

np.array

returns

equivalent rotation matrix

rtype

np.array

References

Geradin and Cardona, Flexible Multibody Dynamics: A finite element approach. Chapter 4