In Windows, I could create a motion graphic with the adobe after effect program. Now I want to know if there is a program in Linux that I can create a simple and beautiful motion graphic?
You can try Blender or Houdini.
You can find Blender in the official repo. I think Houdini is in AUR.
Don’t know if these are what you’re looking for?
Shrek movies are made in Linux, so surely it can. The tools that DreamWorks Animation use to make the movies are however AFAIK proprietary (Autodesk Maya for 3D modeling and a custom render farm to render all the scenes). However, Blender indeed can be used for a single person or a small team project. The rest is your willingness to learn it and the creativity to produce that beautiful motion graphic, like this one: Blender Motion Graphics - 5 Easy Effects in 15 Minutes [Tutorial] - YouTube
Have a look at Synfig Studio
You can try Blender 2.91, The New Grease Pencil is awesome and it’s quite easy to learn as well. Try it and you’ll never regret for what you’ve learned.
As you can see there are some nice solutions for it.
One thing I mis is GIMP in which it is also possible (and not to hard) to create motion graphics with the help of gimp-gap
Krita is another well known program for 2d animations
Another program that has not been mentioned is Natron, which can be installed via AUR. A compositing program which is very close to Nuke and probably what you need if it is After Effects you used.