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-----Original Message-----
From: Jack Uretsky [mailto:jlu@HEP.ANL.GOV]
Sent: Thursday, March 15, 2001 5:26 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Questions & Discussions on Vectors & relationships to
differe ntia l geometry
Hi Joel-
By S1 I mean the circle.
Position on S1 is not a vector (in S1 although it might be
described by a vector in R^2). Circular motion at constant speed -
the velocity vector lies in a tangent space and does not lie in S1,
right? That's exactly what you were asking about, I thought.
For homework, how do you describe the tangent space to S1.
You have to be a litte careful, since S1 is unique among the
spheres Sn of dimension n.
Regards,
Jack
On Thu, 15 Mar 2001, RAUBER, JOEL wrote:
Jack,tranformations involving
I'm not sure I understand your question.
Why do you want to make things so complicated? You
confront all
of these concepts when you consider circular motion.
But my question came precisely from some musing on
rotation plus translation and trying unravel what isgeometric (coordinate
independent) about vectors and what isn't invariant aboutthem or the
vectors we use to represent physical concepts, velocity for example.
Joel Rauber
--
Franz Kafka's novels and novella's are so Kafkaesque that one has to
wonder at the enormity of coincidence required to have
produced a writer
named Kafka to write them.
Greg Nagan from "The Metamorphosis" in
<The 5-MINUTE ILIAD and Other Classics>