中文摘要：

以哈密顿系统、状态空间法为基础的现代控制理论，其数学问题与弹性力学的某些问题具有相似的结构．为了得到微极弹性理论平面问题的通解，本文建立了微极弹性理论平面问题的哈密顿状态方程，并对此方程实施分离变量法得到方程的通解．本方法的特色在于越过了弹性力学问题通常采用的半逆法而直接得到问题的解析解．

英文摘要：

Some elasticity problems bear a resemblance to the mathematical structure of modern control theory, which is based on Hamihonian system and state space method. To achieve the general solutions to planar micropolar elasticity, Hamihonian state space equations are derived and variables separation method is applied. This new method provides a direct approach to the general solutions analytically, instead of resorting to the semi-inverse method, which is traditionally used in solving elasticity problems.