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.