# Proving Euler-Lagrange for constrained system

1. Feb 15, 2013

### railblue

1. The problem statement, all variables and given/known data

Given two Euler-Lagrange systems with generalized coordinates $r_1$ and $r_2,$ and input $u_1$ and $u_2$. Suppose now that a constraint is placed on them such that $r_1 = f_1(q)$ and $r_2 = f_2(q)$.

Propose a Lagrangian for the constrained system and show that is is also Euler-Lagrange

2. Relevant equations
Where should I even be starting on this type of proof?

3. The attempt at a solution
I do know that the generalized coordinate themselves are constrained now, but do they contribute at all to reducing the degree of freedom?