A system with one particle has the Hamilton function is the vector of the generalized momentum, the vector of the coordinates. denotes an orthonormal system of Cartesian unit vectors. t denotestime. C1 and C2 are constants. m is the mass of the particle.

(ii) Derive a system of three coupled differential equations forthe coordinates as a function of time

H(P1, P2, P3, 11, 12, 13, t)= (P-3C12702 +6Ctr) + 3C2 |r12
P=pie + p2e2+ P3e3
r=me + x2e + 23e3
{e, ez, es}