RE: [CAD_CAM_EDM_DRO] Math for constant speed ellipse - kepler?

Dragging it back up from the past, and it could be a total red herring, but
didn't Kepler the astronomer come up with some theory regarding constant
speed ellipses? (for planetary orbits) I haven't had a chance to look it up
yet could be another starter????

-----Original Message-----
From: Kevin P. Martin [mailto:kpmartin@...]
Sent: 06 January 2003 15:44
To: CAD_CAM_EDM_DRO@yahoogroups.com
Subject: RE: [CAD_CAM_EDM_DRO] Math for constant speed ellipse


I think I have some bad news if you expect to get f(t) in open algebraic
form.
The total circumference of an ellipse cannot be calculated in algebraic form
because it involves the Elliptic integral of the second kind [E(k, phi)
where k
is related to the eccentricity and phi is the angle about the center of the
ellipse], which can only be evaluated using an infinite series (or a
suitable
initial subset of terms giving sufficient accuracy) or by table lookup.

I therefore find it doubtful that the length of a segment of an ellipse
could be
represented in open form, and the same goes for anything involving the speed
of
motion along an ellipse.

Doesn't mean it is impossible though, just unlikely.
-Kevin Martin


Addresses:
FAQ: http://www.ktmarketing.com/faq.html
FILES: http://groups.yahoo.com/group/CAD_CAM_EDM_DRO/files/
Post Messages: CAD_CAM_EDM_DRO@yahoogroups.com

Subscribe: CAD_CAM_EDM_DRO-subscribe@yahoogroups.com
Unsubscribe: CAD_CAM_EDM_DRO-unsubscribe@yahoogroups.com
List owner: CAD_CAM_EDM_DRO-owner@yahoogroups.com, wanliker@...
Moderator: jmelson@... timg@... [Moderator]
URL to this group: http://groups.yahoo.com/group/CAD_CAM_EDM_DRO

OFF Topic POSTS: General Machining
If you wish to post on unlimited OT subjects goto:
aol://5863:126/rec.crafts.metalworking or go thru Google.com to reach it if
you have trouble.
http://www.metalworking.com/news_servers.html

http://groups.yahoo.com/group/jobshophomeshop I consider this to be a
sister site to the CCED group, as many of the same members are there, for OT
subjects, that are not allowed on the CCED list.

NOTICE: ALL POSTINGS TO THIS GROUP BECOME PUBLIC DOMAIN BY POSTING THEM.
DON'T POST IF YOU CAN NOT ACCEPT THIS.....NO EXCEPTIONS........
bill
List Mom
List Owner



Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/