Nomenclature Question

  • #1

Main Question or Discussion Point

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 [tex]p_{i} = \frac{\partial L}{\partial \dot{q_{i}}}[/tex]

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

Answers and Replies

  • #2
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  • #3
Matterwave
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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
Thank you both.
 
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