Generally, motion capture of that sort does need two or more cameras—the tracker must triangulate the object’s position in space, and if there is little or no paralax shift, there must instead be multiple different perspectives on the object.
That said, it is possible to get an object solve from a single camera, if the object being tracked has enough detail and shifts its orientation enough. I unfortunately do not know Matchmover, though, so I can’t help you with specific steps. I’ll walk through two ways of doing it in PFTrack, and maybe you can figure out how to get equivalent results with Matchmover.
First, for object tracking, create a mask around the object you want to track. Not too tight, as you want the software to be able to see the edges of your object, but tight enough that it won’t get confused by extraneous motion from your actor or other objects moving in the scene. Invert the mask so that it is masking out everything except the object to be tracked.
Create a new motion group, and set the camera to stationary.
Create several user features (aka supervised trackers) in the motion group you created and track each one the length of the clip. Once you have 6 - 8 such features, run a solve for object motion. Hopefully you’ll get some kind of reference that verifies the motion of your object.
Export your scene in your 3d program’s format, manipulate your geometry to match the point cloud, and parent the geometry to the cloud. It might now move the way you want it to.
The other way to do it is through geometry tracking. Start by modelling a tracking object that roughly matches the shape of the object to be tracked. In your tracking program, make a new motion group for your object, and set the camera to stationary. Import the tracking geometry and manipulate it so that it fits as perfectly as possible over the object you want to track. Track the scene; your geometry should reproduce the motion of the object you are tracking.
Export the scene, and in your 3d program, parent your rocket launcher model to the tracking geometry.
There are definitely some “gotchas” in this process, though. The smaller (or further away) the object you’re trying to track is, the less likely it is that you’ll get a good (or any) solve. Also, if there are an insufficient number of reference points on the object, it will be far more difficult. I learned recently that the sort of tracking markers that work great for a camera solve aren’t so good for geometry tracking–texture tends to be better than X’s made from tape in that case.
I don’t have any idea if any of that will be helpful to you working in Matchmover or not, but I hope it is.