Differentiation of conic section equation

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Homework Help Overview

The discussion revolves around the differentiation of a conic section equation, specifically focusing on the time derivative of a particular equation as referenced in a textbook. Participants are exploring the mathematical reasoning behind the derivation process.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive a time derivative but encounters complexity and confusion. Another participant expresses curiosity about the derivation process and requests clarification on the original source. There is also mention of a successful derivation by one participant, although details are not provided.

Discussion Status

Some participants are actively engaging with the problem, with one expressing a need for further clarification while another has found a solution. There is a mix of attempts to understand the derivation and sharing of resources, but no explicit consensus on the method has been reached.

Contextual Notes

One participant references a specific textbook as the source of the equation in question, which may influence the interpretation and approach to the problem. The original poster's struggle with the complexity of the equation is noted, indicating potential challenges in the homework context.

tauon
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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.

RimvVF6.jpg




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.
 
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Never mind. I got the derivation. I also found out I am blind/can't read.
 
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!
 
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
xAij0s7.png

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

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