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Hello Nico, this sounds like a fun project!
I am more familiar with Rigid Dynamics analysis so I would start there.
One idea is to design an axe throwing machine. Imagine something like a closed-end tube that the axe handle sits in. The tube is angled back -80 degrees from vertical with the axe handle in the tube. The tube accelerates forward and rotates just like your hand does when throwing an axe. The tube decelerates and stops angled forward at 80 degrees from vertical while the axe handle slides out of the tube and launches into space.
By designing an axe throwing machine, you will have a standard “test fixture” to throw different axe shapes in exactly the same way to study how axe shape and mass distribution affect the trajectory.