Understanding Angular Momentum and Energy Equations

[LCSphysicist]

Homework Statement

1. Obtain Eqs.(9.7a and b) by differentiating Eqs.(9.8a and b) with respect to time.

Relevant Equations

Aceleration in a polar coordinates and energy and momentum angular in a central force motion

Since the equations are, actually, the question, i will post the image with relevant equations here:

it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms

 

[haruspex]

Homework Statement:: 1. Obtain Eqs.(9.7a and b) by differentiating Eqs.(9.8a and b) with respect to time.
Relevant Equations:: Aceleration in a polar coordinates and energy and momentum angular in a central force motion

Since the equations are, actually, the question, i will post the image with relevant equations here:

View attachment 262151
it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms

Did you remember to differentiate $r^2\dot\theta^2$ using the product rule?

 

[LCSphysicist]

Did you remember to differentiate $r^2\dot\theta^2$ using the product rule?

Yes, will post soon.

 

[LCSphysicist]

[This solution is actually equal to my solution, which is, unfortunately, not equal to equation nine.seven a]

Assuming theta two dots equal zero.

 

[haruspex]

Yes,

No, you didn't.

Assuming theta two dots equal zero.

Why would you assume that?

 

[LCSphysicist]

No, you didn't.

Why would you assume that?

I did, just cutted the therm with theta two dots and so don't put in the resolution:

call theta by a
(r²a²')' = 2rr'a²' + 2r²a'a'', if a'' is zero, = 2rr'a²' like the image

But stopping to think now, i really see that [theta]'' is not zero, how to deal with that term?

 

[LCSphysicist]

Wow, using L = mw²r i got the answer! thank you