Differential equations – How do you solve these ODEs with NDSolve?

The calculation changes t = 0 there sin[ψ

eq1 = ω1
eq2 = ω2

and construct the linear combinations,

eq1n = Simplify[eq1Sin[eq1Sin[eq1Sin[eq1Sin[ψ
(* Cos[ψ

(If this were not possible, the equations themselves could not be solved in principle.)

Now replace eq1, eq2 by eq1n, eq2n,

I1 = 2; I2 = 3; I3 = 4;
s = NDSolveValue[{I1*ω1'[{I1*ω1'[{I1*ω1'[{I1*ω1'
I2 * ω2 & # 39;
I3 * ω3 & # 39;
eq1n == 0, eq2n == 0,
ω3
ω1[0] == 2, ω2[0] == 3, ω3[0] == 4, ψ[0] == 0, φ[0] == 0, θ[0] == Pi / 6},
{ω1
plot[Evaluate@s[[1 ;; 3]], {t, 0, 120}, ImageSize -> Large]plot[Evaluate@s[[4 ;; 6]], {t, 0, 120}, ImageSize -> Large]

Enter the image description here

Enter the image description here

Incidentally, the original equations can be solved by slightly changing the initial state ψ[0] == 0 to ψ[0] == 10 ^ -6,

Another approach is to use the option.

Method -> {"EquationSimplification" -> "Residual"}

Everyone gives the same answer.