# Nomenclature Question

1. Dec 10, 2014

### snatchingthepi

So I'm studying for my CM final and in looking over the section on ignorable coordinates and generalized momenta I come across the definition for conjugate momentum $$p_{i} = \frac{\partial L}{\partial \dot{q_{i}}}$$

My question is simple - why is it called 'conjugate'? I just never really thought to question to the name.

2. Dec 10, 2014

### Staff: Mentor

3. Dec 11, 2014

### Matterwave

You need a word to differentiate it from a physical momentum, I guess "generalized momentum" might also work, but the "conjugate" part comes into play more when you move to Hamilonian mechanics where your phase space coordinates are these (p,q) conjugate pairs.

4. Dec 11, 2014

### snatchingthepi

Thank you both.