How to solve $F(t)=A(t)F'(t) ,F(0)= I\tag 1$
- All are $3 \times 3$ matrices except variable t
- A(t) is given and has determinant $0$. $A(t)=(I-tC_1)^{-1}t^3C_2 \tag 2$
- I is a constant unit rotation matrix means I is unity matrix
- $C_1,C_2$ are constant skew symmetric matrices of $0$ determinent
$$C_1=\left( \begin{array}{ccc} 0 & -c_0 & b_0 \\ c_0 & 0 & -a_0 \\ -b_0 & a_0 & 0 \\ \end{array} \right).$$ $$C_2=\left( \begin{array}{ccc} 0 & -(c_1-c_0) & (b_1-b_0) \\ (c_1-c_0) & 0 & -(a_1-a_0) \\ -(b_1-b_0) & (a_1-a_0) & 0 \\ \end{array} \right).$$
NB: All entries of the matrices $C_1$, $C_2$ are constants,can't be altered