It would be excellent to have a prescribed rotational translation in addition to the prescribed linear translation.
In the axe head example, the axe travels in a linear fashion straight down. This is not true-to-life, though. Similarly, any motion of striking by an axe, hammer, or similar would likely have rotation instead of linear motion.
This translates to a more complicated result, but a more realistic one. Drop tests with rotation applied would show true bounce and tumble as well.