So here's a TAS frame by frame analysis of the different ways to do the rocket dash/rocket boost/aerial super wavedash.
(Note: This is the most optimal way of preforming this technique meaning you will go the farthest. You can get this technique to work fine as long as frame 1, you're holding the control stick generally towards the platform, up/down doesn't matter, frame 2 you're holding the control stick generally away from the platform, up/down doesn't matter, and frame 3+, you're holding the control stick generally towards the platform.)
The green suit samus is controller 1, the normal samus is controller 2.
The inputs are basically representing what the control stick of each controller is doing. (Regular grey analog stick on the left, c-stick on the right)
So these 2 different ways of inputting the technique have the exact same result, but for some people the green samus' inputs might be easier.
You either input down and toward the platform, or you slightly tilt the analog stick towards the platform the first frame.
Assuming your analog stick was in the neutral position the frame before and you are in bomb animation on the edge of a platform as shown, this should be the first input:
(Note: This rocket boost is not being preformed on the first possible frame it could be so if it was preformed earlier in the bomb animation you could theoretically go farther.)
Second frame/input of the technique:
Both the green samus and normal samus are smashing all the way away from the platform they're on.
Third frame input:
After you've smashed all the way away from the platform on the third frame you do the same input you did on the first frame. Either holding down and towards the platform or tilting towards the platform.
For all other frames of the bomb animation you have to keep holding in this position or you will stop immediately.
Here's frame 4:
As you can see, still holding the same input and still flying.
And the final frame (once the bomb animation is over):
You can see both Sami went the same distance even though they did different inputs.
I cut some custom notches in my controller to do exactly what the green samus did. I've found it's hard even at 1/4 speed in training mode to do the tilting method. I've found sometimes that tilting back the first frame and holding down and towards the platform on the third frame+ is another way of inputting if you're more comfortable with that.
Another thing: depending on how optimally you do it (meaning if you do the exact same inputs as the images) you will have more leniency of how far away from the edge of the platform you can preform this technique and still go flying. If you do it completely perfectly you can start in bomb animation in about the center of the pokemon stadium platform and still go flying. If you're just trying out learning it then try rolling to the edge of the platform, dropping through and bombing (that's what I did to set up this TAS).
If you let the analog stick return to neutral while you're flying you will immediately stop. This gives you more options if you preform it optimally, because you can basically choose at what point you'd like to stop, whereas if you did it non-optimally you could only go a certain distance before you stopped just from the animation ending.
If you are considering trying to learn this technique, be warned: At full speed it's even a little harder than the Short Hop Fast Fall Missle Cancel.
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How this technique works (this is most likely an asinine explanation, but this is just my theory):
Like the superwavedash, this is an exploit of the daughter dash mechanic. The daughter dash essentially teleports you small distances as samus while she's on the ground and in bomb animation.
The mechanics of being in bomb animation on the ground and in the air work differently.
The way the regular superwavedash works is that you do a daughter dash on the very last frame you're in ground-bomb physics. Normally you would just do a single daughter dash (what some people refer to as "SWD too early"), but because you're no longer in ground bomb physics once you've already moved, you retain your momentum from the daughter dash.
The rocket boost works similarly, but instead of transitioning from ground bomb physics just to "regular game physics", you transition from ground bomb physics to air bomb physics.
So if you do a daughter dash off of a platform then you transition from one type of physics to another. For SOME REASON (I honestly have no idea) you have to "trick" the game into thinking you're still in ground bomb physics by holding the control stick towards the platform. This way you can keep the momentum from the daughter dash.
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Anyways, I hope you all start learning how to rocket dash!