crv2tan

Returns the tangential operator, \(\mathbf{T}(\boldsymbol{\Psi})\), that is a function of the Cartesian Rotation Vector, \(\boldsymbol{\Psi}\).

\[\boldsymbol{T}(\boldsymbol{\Psi}) = \mathbf{I} + \left(\frac{\cos ||\boldsymbol{\Psi}|| - 1}{||\boldsymbol{\Psi}||^2}\right)\tilde{\boldsymbol{\Psi}} + \left(1 - \frac{\sin||\boldsymbol{\Psi}||}{||\boldsymbol{\Psi}||}\right) \frac{\tilde{\boldsymbol{\Psi}}\tilde{\boldsymbol{\Psi}}}{||\boldsymbol{\Psi}||^2}\]

When the norm of the CRV approaches 0, the series expansion expression is used in-lieu of the above expression

\[\boldsymbol{T}(\boldsymbol{\Psi}) = \mathbf{I} -\frac{1}{2!}\tilde{\boldsymbol{\Psi}} + \frac{1}{3!}\tilde{\boldsymbol{\Psi}}^2\]

param psi:

Cartesian Rotation Vector, \(\boldsymbol{\Psi}\).

type psi:

np.array

returns:

Tangential operator

rtype:

np.array

References

Geradin and Cardona. Flexible Multibody Dynamics: A Finite Element Approach. Chapter 4.