If you have Premiere Elements 11 with its Time Remapping feature, give this a try for the task that you described. The feature accepts video, but not Time Stetched files, photos, titles, or Instant Movie types. It should accept your animation.mov file so that you can set the Time Zones of the feature, each with its motion set. I wonder if it can be set fast enough for your purposes.
Overview - Adobe TV Video Tutorial
The feature can be accessed from the Tools Menu at the top of the Expert view interface or via the Tools Tab at the bottom of the Expert view. It opens to its own workspace. See below.
The "Extremely Fast 8X" setting translates into fast motion with Speed % = 800 (every 8 frames become 1 to shorten). This feature allows you to apply varying motion effects across a single clip without having to cut the clip. The Time Zones are the segments. Although Premiere Pro uses "Speed keyframes" for its Time Remapping, I cannot as a user find any keyframes in that sense. Please ignore the description if you have been there and done that already.
Also, the featue does not deal with audio. It is left as is as the video file duration is increased or decreased in response to your Time Remapping of the video portion.
Please let us know the outcome.
Thanks for the input, Romano, but I've already done quite a bit of Time Remapping. My problem here is to get a smooth transition from a minor spead-up to a major spead-up in a mathematically-graduated transition. There's no mechanism to accommodate that in the Time Remapping tool. You have a specific time from beginning to end of your keyframing on the video, and that's it.
I compromised and set up a series of the exact same video, with size, opacity, and speed dimminishing from first clip to last. Not what I'd hoped for, but it works to some extent.
I'm now up to Take 144. Will be putting in the live videos from The Strip next week, and will probably have Take 150 onto YouTube some time in early August.
Also hope that my pal Serj Tankian of System of a Down (SOAD) will let me use some of his recent compositions for background music. He's a brilliant composer.
Again, thanks for your help.
Has your Time Remapping been exclusively with Premiere Pro or have you also looked at this in Premiere Elements 11.
The reason that I ask has to do with the keyframing of the Speed property that does exist in Premiere Pro with its Time Remapping which allows for variable motion across the clip without having to cut the clip at points for your ramp motion as you would need to do with Time Stretch to get the ramp motion.
But as far as I have been able to dig out of the Premiere Elements 11 Time Remapping, there is no keyframing of the Speed. It gives all the appearance of being driven by the increase or decrease in video frames, as governed by the Speed % change from 100% as does Time Stretch.
Based on your project requirements you do not seem to feel that Time Remapping (wherever) will serve your purpose. Have you zero'ed in on a program with feature that can do the task that you envision.
I'm using Premiere Elements 11. There's keyframing in the Time Remapping effect to the extent that you can create a starting point and an ending point for the remapping ... ie you can move the starter somewhere to the middle of the clip and then extend the ending keyframe to a spot short of the end of the overall clip.
But, as you noted, there's no device for graduating the speed.
I wish that Elements had this facilty, but I must live with what is. (My needs don't justify the extra expense of upgrading to Premiere Professional.)
I wish also that the Time Remapping commented on frames per second (fps) as well as time as measured in seconds and decimals thereof. The fps rate would give me a better idea of how clunky an expanded clip would look. As it is, you have to do the remapping, then run the clip to see if it's clunky or not.
Ah, well, as above, life is what it is and I shall live with it.
I think I created a decent workaround, and will show it to you and the others sometime next month.