Optimizing Gear Train Simulation with Exponential Acceleration and Braking

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Hi:
I'm building a computer simulation for a 3 gear train system. So far the gears rotate with mouse movement horizontally. Now I'm adding a fictitious motor and braking system to start/stop rotation with mouse clicks. I multiplied the rotation angle by [1-e(-t/TC)] to simulate exponential acceleration and e(-t/TC) for braking for exponential deceleration. Is exponential is the right way to do it? or is there any other better equation. This is just a simple case with no other external conditions influencing; but just the system inertia.
In general terms this is the equation I'm using.
Acceleration=[1-e(-t/TC)];// acceleration case
Acceleration=[e(-t/TC)];// braking case

Thanks
 
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The meshed gears will have kinetic energy proportional to RPM squared.
The motor will provide that energy. You must specify the Torque to RPM curve for the motor.

Power = torque * RPM = watts = joules of energy per second.
Use that to compute the change in velocity over time as energy flows in or out.

There will be some energy losses that will remove energy and so reduce the RPM. Ignore them for now, or make them proportional to RPM.
 
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Hi:
Interesting info. I'll experiment trying to code that somehow (?) and see the results. My goal is just having an acceptable "visual effect", although using the real equation will be much better.
The real question would be: What is the equation for the change in rpm with time (angular acceleration)? I assumed it to be exponential so it will tend to the end value asymptotically with time in both cases.
Thanks
 
Wow that is awesome!. Thanks.