Question about the modeling part

[JackLiujie]

How to transform the state space formalism into discrete-time state-space system？ I didn't understand the step。 In the discrete-time state-space system, we can get : ddot_theta(k+1)= ddot_theta(k) +(D/(2I))(U1(k)-U2(k)), why not "ddot_theta(k+1)= (D/(2I))(U1(k)-U2(k))" from the first Newton's second law equation?