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Topic: Re: Locus for ratio of cosine of angles to be constant
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Posts: 359
Registered: 9/16/06
Re: Locus for ratio of cosine of angles to be constant
Posted: Nov 17, 2013 10:44 AM
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cos(s) = cos(p) ecc where ecc is a constant.

Use differential relations between r,th (polar) and x,y (cartesian) coordinates with respect to arc length s.

dr/ds - dx/ds ecc = 0 which integrates to

r - x ecc = r - r cos(th) ecc = p, an arbitrary constant.

1 - ecc cos(th) = p/r the polar equation of all conics.

Given constant is eccentricity and arbitray constant is semi-latus rectum.

This rotational definition imho is much better than the standard distance definition of conics with respect to the meaning and significance of eccentricity.


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