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Re: [Phys-l] bound vectors ... or not



On 09/07/2010 02:47 PM, Edmiston, Mike wrote:

www.bluffton.edu/~edmistonm/ConstantTorque.pdf

Very nice.

these are actual devices that have utility in the engineering of
real products.

Another place where the same line (so to speak) of
reasoning shows up is in aerodynamics. Replace
the linear force actuator by an engine+propeller.
Consider the top drawing as a front-engine design
and consider the bottom drawing as a rear-engine
design. The pitching moment will be the same in
either case.

Being able to glance at situations like this and
appreciate the invariances is a valuable skill.

==========

There are about ten good ways to think about this.
One way that appeals to me is to represent the
torque as a bivector. The magnitude of the torque
is the area of a parallelogram, which is invariant
with respect to shearing the parallelogram. YMMV,
but for me this is very visual and very intuitive.
It's way better than cross products.