Differentiation of conic section equation

[tauon]

Homework Statement

I do not understand how the authors got the time derivative of equation 1.5-4 in the form given at 2.5-2.

Homework Equations

The Attempt at a Solution

$$\frac{d}{dt}\frac{p}{1+e cos\sigma}=-\frac{p}{(1+ecos\sigma)^2}(-esin\sigma\dot\sigma)=\frac{pe\, sin\sigma\dot\sigma}{1+2e\,cos\sigma+e^2cos^2\sigma}$$

?

I tried various rewrites using trigonometric identities, but the equation just got so complicated that it'd take me a long time to typeset it in this post.

 

[tauon]

Never mind. I got the derivation. I also found out I am blind/can't read.

 

[geoffrey74]

Hi tauon! I'm curious if you could share how you got the derivation, or which textbook your above excerpt is from. I'm trying to get to equation 2.5-2 from this excerpt, but seem to be getting stuck the same spot you were. Thanks!

 

[tauon]

Hi. This might be very late now, but I didn't check this thread since I got the solution. :p
In case someone runs into it in the future, this is the derivation I used

Oh, and the excerpt is from "Fundamentals of Astrodynamics" (authors Roger Bate, Donald Mueller, and Jerry White) the 1971 edition.