Calculation of NonUniform Circular Motion

[rfdes]

Hi -
I have a problem that somewhat mimics an
orbital mechanics problem, but I'm struggling
with seeing the light. My engr math is very
rusty and could use some insight.

Problem Description:

Assume a point rotating non-uniformally
on the circumference of a circle, similar to
a planet around the sun. The exception being
the rotation is at a constant radius. Now,
assume that non uniform time is measured between
points A,B & C, where A,B & C are exactly 120 degrees
apart. So t(AB),t(BC),t(CA) are different.

Is there a closed form equation that would calculate
the resultant vector? Not sure I am explaining this
properly and this may be a very simple exercise in
trig/geometry, however, I cannot seem to figure this
out. If someone is familiar with this, I should could
use some help. Thanks.

Jim

 

[Petyab]

Is that all the information that's given? If they're 120 degrees apart with a variable circle r then you can split the circle into segments and integrate the x values as a function of y using some clever connection to arclength=sr(theta) and the integral. Given time and and 120 degrees apart you could be talking about a spider monkey's elbow so I think you need more information.