this question from In V.I.Arnold's book about ordinary differential equations. I'm having difficulty with problem after the example of small oscillations of a spherical pendulum can please help me for the problem.the problem is prove that the phase curves are great circles of these spheres however, not every great circle of a sphere is a phase curves.
We have the system of differential equations $$ x'_1=x_2 \quad x'_2=−x_1\\ x'_3=x_4 \quad x'_4=−x_3. $$
please help me to solve this problem. thanks
