(4) -A :q_k + K .p_k = Ta(q_k - s_k) + Ta[q_k - s_(k+1)],
(5) A :p_k + K .q_k = -Ta(p_k - r_k) - Ta[p_k - r_(k+1)];
and for the motion of translation
(6) M :x_k = T[r_(k+1) - r_k], M :y_k = T[s(k+1) - s_k];
while the geometrical relations are
(7) x_(k+1) - x_k = a [p_(k+1) + p_k] + 2lr_(k+1),
(8) y_(k+1) - y_k = a [q_(k+1) + q_k] + 2ls_(k+1).