Re: Problem

[Bob Sciamanda <trebor@VELOCITY.NET>]

> . . . The
> time derivative of any vector is another vector which can always be
> decomposed into parallel and transverse (to the direction of the
original
> vector) components.  The parallel component affects only the magnitude
of
> the original vector - and is in fact equal to the rate of change of that
> magnitude.  The perpendicular (or "turning") component leaves the
> magnitude of the original vector unaffected and affects only the
direction
> of the original vector.

A useful corallary :
The derivative of any unit vector is perpendicular to the original unit
vector direction.  This a priori knowledge eases the students'
consternation in calculating vector derivatives in non-Cartesian basis
vector systems.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor