# Finding Conserved Quantities of a Given Lagrangian

1. Feb 19, 2013

### pcvrx560

1. The problem statement, all variables and given/known data
Find two independent conserved quantities for a system with Lagrangian

$$L = A\dot{q}^{2}_{1} + B\dot{q_{1}}\dot{q_{2}} + C\dot{q}^{2}_{2} - D(2q_{1}-q_{2})^{4}\dot{q_{2}}$$

where A, B, C, and D are constants.

2. Relevant equations
None.

3. The attempt at a solution
I've only found one symmetry,

$$q_{1}\rightarrow q_{1}+C$$
$$q_{2}\rightarrow q_{2}+2C$$

with the corresponding conserved quantity

$$2\dot{q_{1}}(A+B) + (B+4C)\dot{q_{2}} - 2D(2\dot{q_{1}}-\dot{q_2})^{4}$$

The other symmetry and conserved quantity is not so obvious to me.

This is actually a homework assignment I got back and am looking over for a test.

Last edited: Feb 19, 2013