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Carbon for Houdini and Carbon Cloth for Maya now include Timescale and Timewarp functionality to help with the manipulation of time,
for slow mo effects etc.

Below is a video generated from the example, downloadable from the Carbon docs.
First here are the animation graphs controlling what is happening in the video.

The animation graph for simulation time warp and time scale:

step

Animation curve for the rotation around the X axis:

anim

 

As you can see, they are perfectly in synch, i.e. when time scale and time warp jump from 1 to 0.2, the animation instantaneously slows down
from 1 rotation per 60 frames to 1 rotation per 300 frames, i.e. a factor of 5. And so on...
Note that we purposely put in instantaneous transitions to be able to show the difference in behavior much clearer.

Time Warp:
If you want to create a slow motion effect, this is probably what most people have in mind and should be using.
Time warp actually changes the simulation frequency; in contrast to time scale, which only scales all time dependent parameters.
Very important: Geometry animation (such as colliders, reference pose, goal pose, etc) needs to be in synch with the time warp animation!

Time Scale:
If you have an animation frequency of let's say 240 Hz fixed, but want to make the simulation behave as if the animation was in 24Hz,
you will want to use Time Scale. You cannot use time warp here because you do not want to change the animation and simulation frequency.
You just want to change how the ui parameters are interpreted by the solver. This is just like the (length) scale parameter.

Let's look at the green cloth first. This is a "normal" simulation, meaning Time Scale and Time Warp are both set to 1.0.
The behavior is just as expected. Look at some of the most abrupt changes in the tube animation speed.
Slowing down by a factor of 5 at frame 60 causes the cloth to "clash" with the rod as it still carries momentum.
Then later, at frame 420, when the tube starts spinning extremely fast, the cloth starts to stretch due to the centrifugal forces.

Now, looking at the same transition and behavior at frame 420 (fast spinning motion) for Time Scale and Time Warp. 
The cloths do not stretch because of the animated time parameters.

You won't see much of a difference between Time Scale and Time warp when accelerating, but the difference can clearly be seen when
the spinning slows down, such as happens at frame 60 and 540. Time Scale does not affect the momentum of the cloth.
This is why the red cloth slows down much slower than the blue time warp cloth. It's velocity is only affected through physics interactions.
By analogy it is like jumping in the water with a transition phase between moving with low resistance in the air and now moving in the water.
You do not immediately come to a stand still when you enter the water, but your speed is gradually reduced.

TS1

Check out the example in the downloads section of the Carbon Docs....