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
If the coefficients depend only on the spatial variable, we use the distance function to construct the multiplier, and then use the classical comparison theory from Riemannian Geometry to deal with the error terms. 当变系数只依赖于空间变量时,我们用距离函数构造几何乘子,然后用黎曼几何中经典的比较定理来估计余项。