保守力系右式为零，导出欧拉-拉格朗日方程（ **Euler–Lagrange equations | Lagrange's equations of the second kind**）

$Q$是广义力

$$ \left\{\frac d{dt}\left(\frac{\partial L}{\partial\.{q}_j}\right)-\frac{\partial L}{\partial q_j}\right\}=Q_j^{EX} $$

An excluded generalized force $Q^{EX}$ which contains the non-conservative. velocity-dependent 速度相关, and all the constraint force not explicitly included in the potential $U_j$

完整约束右式引入拉格朗日乘子(Lagrange's equations of the first kind )

$$ \left\{\frac d{dt}\left(\frac{\partial L}{\partial\.{q}j}\right)-\frac{\partial L}{\partial q_j}\right\}=\sum{k=1}^m\lambda_k\frac{\partial g_k(\mathbf{q},t)}{\partial q_j}+Q_j^{EXC} $$

the non-conservative generalized force$Q^{EXC}_j$contains non-holonomic constraint forces, including dissipative forces such as drag or friction, that are not included in$U$,or used in the Lagrange multiplier terms to account for the holonomic constraint forces.