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[Phys-L] Re: A problem of motion and derivatives



... to move along an arbitrary path (the simplest example is circular
motion, say a car driving around in a circle), one cannot keep one's
velocity constant. When acceleration is constant for a car moving on a
circular path, the car can keep jerk =0 and end up driving in a tighter or
wider circle if it changes its direction and velocity in a harmonious way so
that their combined contribution to acceleration = some constant. For
example by driving in a tighter circle, one must apply some amount of
braking to keep overall acceleration constant. Is this the case or am I
missing something obvious? Can jerk be kept to 0 in this instance? Can it
be kept to 0 on any arbitrary path between two points?

I think you are have in mind a situation in which the *magnitude* of
the acceleration is kept constant. It is not possible to move along a
circular path with constant acceleration. Constant, non-zero
acceleration necessarily leads to parabolic trajectories. Thus, if
the jerk is kept equal to zero, the path is either a straight line or
a parabola.

--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>
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