A $3$ dimensional vector $v=[w_x,w_y,w_z]$, The product of the vector's null space and the vector itself is given as $J(v^T)*v=0...(1)$ , where $J(v)=\text{null}(v^T)$ and assumed as orthonormal. Now, the vector can be written as $v=\text{inverse}(J(v^T))$
I would like to know the value of $d(v)/dt$.
Whether $d(v)/dt=\text{inverse}(\text{null}((d(v)/dt)^T))$