I tried to solve system of ODEs, but something was wrong.
Clear[P]
Clear[A]
A = {1, 0, 0}
P[t_] = {P1[t], P2[t], P3[t]}
Q[t_] = {Q1[t], Q2[t], Q3[t]}
sol3 = DSolve[{P'[t] == Cross[A, Q[t]], Q'[t] == Cross[A, P[t]],
P[0] == {0.5, 0.5, 0.3}, Q[0] == {0.1, 0.2, 0.3}}, {P[t], Q[t]}, t]
The result is
DSolve::dsfun: {P1[t],P2[t],P3[t]} cannot be used as a function. >>
What interesting for me is that when I try to solve only one equation (not a system), everything is OK:
sol2 = DSolve[{P'[t] == Cross[A, P[t]], P[0] == {0.5, 0.5, 0.3}},
P[t], t]
{{P1[t] -> 0.5, P2[t] -> 0.5 Cos[t] - 0.3 Sin[t],
P3[t] -> 0.3 Cos[t] + 0.5 Sin[t]}}
I don't understand how it works...