Holonomic

Holonomic constraints are $F(x_i,t)$ and can be expressed in generalized coordinates. Can use Lagrange Multipliers

Euler-Lagrange Equation

$$\tilde{L}=L+\sum _j{\lambda }_j{F}_j$$

where

$$F=F(x_i,t)$$ $$\frac{\partial L}{\partial x_i}-\frac{d}{dt}\frac{\partial L}{\partial {\dot{x}}_i}+\sum _{j=1}^n{\lambda }_j(t)\frac{\partial F_j}{\partial x_i}=0$$