Q: Use Poisson Brackets to show that $Q$ generates the transformation $q_i \to q_i +a$ where $a$ is a constant and $i=\{1,2,3\}$ I am given the Lagrangian $L= \frac{1}{2}(\dot q_1^2 +\dot q_2^2 + \dot q_3^2) -e^{q_1-q_2} - e^{q_2-q_1}$
And firstly I am asked to find what $Q$ is, using Noether's theorem under the transformation
$q_i \to q_i +a$ where $a$ is a constant and $i=\{1,2,3\}$
So I showed that this transformation was invariant and got the $Q = \dot q_1 +\dot q_2 + \dot q_3$
Then the question asks me to express Q as canonical momenta, now I am not really sure what this means, so I guess it meant put $Q =p_1 +p_2 +p_3$
Then the question asks me to find 2 functions $A$ and $B$ and use the poisson brackets $\{A,B\}$ to show that $Q$ generates the transformations earlier specified.
So I guess that one of the functions must be $Q$ but I don't know how to figure out what the other function should be to get the transformations required.
