中文摘要：

考虑垂荡运动和波浪激励力矩的双重影响，建立Spar平台参一强联合激励下的纵摇运动方程。应用摄动法求得当垂荡频率与纵摇固有频率比接近2：1时纵摇方程的一阶近似解，并分析了方程零解与定常周期解的运动稳定性。以一座试验Spar平台为例，计算了该平台在长周期涌浪下纵摇运动的时域响应。

英文摘要：

The parametric and forcing excited differential equation for pitch motion of a Spar platform is established with considering the effects of heave motion and wave exciting moment. The first-order approximate solution of the Mathieu equation is solved by the pertur- bation method when the heave frequency is approximately double the pitch natural frequency. The stabilities of trivial solution and steady-state periodic solution are analyzed according to the nonlinear dynamic theory. As a example, the pitch response of a spar model is obtained under long periodic swell.