Hamilton’s equations of motion → Hamilton's canonical equations哈密顿正则方程

$$ \begin{align}\.{q}{j}& =\frac{\partial H(\mathbf{q},\mathbf{p},t)}{\partial p_j} \\ \.{p}{j}& =-\frac{\partial H(\mathbf{q},\mathbf{p},t)}{\partial q_j}+\left[\sum_{k=1}^m\lambda_k\frac{\partial g_k}{\partial q_j}+Q_j^{EXC}\right] \\ \frac{dH(\mathbf{q},\mathbf{p},t)}{dt}& =\sum_j\left(\left[\sum_{k=1}^m\lambda_k\frac{\partial g_k}{\partial q_j}+Q_j^{EXC}\right]\dot{q}_j\right)+\frac{\partial H(\mathbf{q},\.{\mathbf{q}},t)}{\partial t} \end{align} $$

$$ \frac{\mathrm{d}f}{\mathrm{d}t}=\{f,\mathcal{H}\}+\frac{\partial f}{\partial t}, $$