Why is momentum referred to as 'conjugate' in physics?

[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.

 

[jedishrfu]

The best I can come up,with that since the momentum is paired with the generalized coordinates of the system then conjugate is used to describe that fact.

http://www.merriam-webster.com/dictionary/conjugate

 

[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.

 

[snatchingthepi]

Thank you both.