Discretization of the Euler Top

The Euler top described by the equations \(I_1{{ d} ω_1}{{ d} t}=(I_2-I_3)ω_2 ω_3\), \(I_2{{ d} ω_2}{{ d} t}=(I_3-I_1)ω_3 ω_1\), \(I_3{{ d} ω_3}{{ d} t}=(I_1-I_2)ω_1 ω_2\), is discretized in the following form \(I_1[ω_1(t+δ)-ω_1(t)] =12 δ (I_2-I_3)[ω_2(t+δ)ω_3(t)+ω_2(t) ω_3(t+ δ)]\), \(I_2[ω_2(t+δ)-ω_2(t)] =12 δ (I_3-I_1)[ω_3(t+δ) ω_1(t)+ω_3(t) ω_1(t+ δ)]\), \(I_3[ω_3(t+δ)-ω_3(t)] =12 δ (I_1-I_2)[ω_1(t+δ) ω_2(t)+ω_1(t) ω_2(t+δ)]\), which exhibits conserved quantities and exact solutions.