Discretization of the Euler top

The Euler top described by the equations I(1)d omega(1)/dt (I-2 - I-3)omega (2)omega(3), I(2)d omega(2)/dt = (I-3 - I-1)omega(3)omega(1), I(3)d omega(3 )/dt = (I-1 - I-2)omega(1)omega(2), is discretized in the following form I- 1[omega(1)(t+delta)-omega(1)(t)] = 1/2 delta(I-2-I-3)[omega(2)(t+delta)omeg a(3)(t) + omega(2)(t)omega(3)(t + delta)], I-2[omega(2)(t + delta) - omega( 2)(t)] = 1/2 delta(I-3 - I-1)[omega(3)(t + delta)omega(1)(t) + omega(3)(t)o mega(1)(t + delta)], I-3[omega(3)(t + delta) - omega(3)(t)] = 1/2 delta(I-1 - I)[omega(1)(t + delta)omega(2)(t) + omega(1)(t)omega(2)(t + delta)], whi ch exhibits conserved quantities and exact solutions.