Omega={{0,-omega,0},{omega,0,0},{0,0,0}};
Id={{1,0,0},{0,1,0},{0,0,1}};
A=Id+Sin[omega*t]/omega*Omega+2*(Sin[omega*t/2]/omega)^2*Omega.Omega
            
F=Simplify[Id*t+(1-Cos[omega*t])/omega^2*Omega-(Sin[omega*t]-omega*t)/omega^3*Omega.Omega]
