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p_1(t) = p_i - \int_0^t p_{u,\rm 11}(t-\tau) dq_1(\tau) - \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) = \rm const

\dot p_1(t) = - \left( \int_0^t p_{u,\rm 11}(t-\tau) dq_1(\tau) \right)^{\cdot} - \left( \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) \right)^{\cdot} = 0

 p_{u,\rm 11}(0) \cdot q_1(0t) + \int_0^t \dot p_{u,\rm 11}(t-\tau) dq_1(\tau)  = - p_{u,\rm 21}(0) \cdot q_2(0t) -  \int_0^t \dot p_{u,\rm 21}(t-\tau) dq_2(\tau)