Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am going through the solution for a problem (1.7 from Goldstein's Classical Mechanics) where it says:

enter image description here

I don't understand why the right-hand side of the second line only contains 4 terms when there should be 5. The very last term on line 1 has been expanded into 1 term on line 2 using the product rule, but according to the product rule there should be 2 terms.

share|improve this question
1  
Why "0% accept rate"? –  AlbertH Jul 27 '12 at 6:57
    
Oh, I was informed that the accept button is mainly for the stackoverflow people, who have to test their code to see what works. Anyhow, I shall go ahead and start using it. –  Joebevo Jul 27 '12 at 7:30
add comment

2 Answers

up vote 1 down vote accepted

$q$, $\dot{q}$ and $\ddot{q}$ are being treated here as separate variables, so $\dfrac{\partial \ddot{q}}{\partial \dot{q}} = 0$.

share|improve this answer
add comment

I think this results from: $$ {\frac {\partial {\dot q}} {\partial {\dot q}}} = 1 $$ Hence: $$ \frac {\partial {\ddot {q} }} {\partial \dot q} = \frac {\frac {\partial {\dot q}} {\partial t}} { \partial {\dot q} } = \frac {\partial( \frac {\partial {\dot q}} {\partial q}) }{\partial t} = \frac {\partial 1} {\partial t} = 0 $$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.