Determining Future Position of Uniform Circular Motion

[Arjan82]

So you've found a solution not using branching, but indeed adapting t0. That seems to be correct indeed.

 

[Cato11]

Thank you very much for the in-depth explanation, I think most of it made sense and it reflects what I was seeing as I attempted the branching method.

I definitely prefer the second method of adapting t0 as it's a lot simpler. I've also tried it with neat and messy angles like 74° and it always seems to produce the correct results. Phew!

So I take it this second method can be reliably trusted?

Also, any idea how to adapt this for clockwise motion? Is it simply a case of flipping the "polarity" variable?

 

[Arjan82]

Also, any idea how to adapt this for clockwise motion?

I'll leave that as an exercise to the reader ;)

 

[Cato11]

I'll leave that as an exercise to the reader ;)

Ah.. fair enough!

But regarding the second method of adapting t0. Do you believe this to be a reliable one? You mentioned with the first method of branching that messy things could be going on.

 

[Arjan82]

I mentioned that because I could not oversee the consequences of the combination of the two t0's you've computed and all variations of the general formula you've used in the first solution (maybe one quadrant ran backwards for all I knew) I didn't check that.

But you can check that yourself. If the starting points in all quadrants give correct results, if small additions in the starting position (1 degree, say) give the same difference in the future point, and if the connections are continuous (so at both sides of the point when Y of the startingpoint flips sign) then your solution works.

You can also try to reason why using the polarity works by writing down examples for all quadrants and see what the computation of t0 yields, looking at the range of acos(). Then it should be easy to see why the polarity works (if indeed it does, I didn't check it).

 

[Cato11]

Thank you Arjan. I have done some pretty extensive testing today, checking for continuity as Y flips sign and also that small and large variations in the start point propagate to the future point. The updated function has yet to make a mistake so I'm happy to report that the solution works.

It took a while but got there in the end! Thank you again for all of your help