## Mathematical problem (syncing variable speed phasors)

Sep 06 2020 | 6:15 pm

Hi all!
I
'm just stuck with a mathematical problem i need some help to solve. Let's see if i can explain it properly:

I have 2 synced phasors, at the same frequency and phase.

At some arbitrary moment, i want phasor A to accelerate for 4 seconds until it arrives to, let's say, double the frequency of phasor B.

Phasor A stays at this new higher frequency for some time, and it decelerates for 4 seconds until it reaches again the original frequency.

The problem comes because i want that when phasor A finishes deceleration, it matches the exact phase of phasor B. This obviously means that the deceleration has to start in a specific moment in time to be able to catch phasor B in its exact phase.

I think this is related to uniformly accelerated linear motion equations, and might imply the use of derivative calculous?

I want to use this to sync 3 vertical scrolling image slides, where i want each of the 3 scrolls to alter its frequency from time to time, but then going back to normal speed and matching the exact position of the other 2 scrolls.

I imagine this might be useful to sync audio loops too: having 2 rhythm loops synced, and one starts to accelerate until it reaches double the frequency of the other one, and then going back to normal and catching phase again (beat or bar synced)

Has anyone done something like this and can point out possible solutions?My calculous is pretty oxidized and i don't know how to approach the problem....