crv2tanΒΆ
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.