The Hamiltonian dual differential equations for thick plates are derived and the functional expressions of Hamiltonian variational principle are obtained using the variable substitution and multiplier method . Two orthogonality relationships of the thick plate theory are proposed and demonstrated .

首先导出了厚板哈密顿对偶微分方程，然后采用换 元 乘 子法导出了厚板哈密顿变分原理的泛函表示式，最后提出并证明了厚板理论的两个正交关系。

The control variable namely darg and lift were treated as continuous piecewise linear functions of the negative specific energy . By the Runge Kutta methods the trajectory optimization problem was transferred to nonlinear programming which was solved by Generalized Lagrange Multiplier .

通过将气动力假设为能量参数的分段连续线性函数，并且采用 RungeKutta数值计算方法，将轨迹优化问题转化为多维非线性规划问题，应用广义 乘 子法对其进行数值求解。

Generalized Variational Principles with Several Arbitrary Parameters and the Variable Substitution and Multiplier Method

含多个任意参数的广义变分原理及换 元 乘 子法