Uhm folks... it's called "Chopfit" and it's a long-time standard exercise. A good four or five pound axe has its weight multiplied by the swinging motion, resulting in a good upper body workout to go with the lower body one gets walking/jogging.
One company even makes them that just look like an axe, but are not.
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Not an unusual thing at all. I know a few pro weightlifters who do this all the time.
Nice to know there is a name and explanation, but those of us who come from countries where carrying a potential weapon is NOT normal would quietly turn around .
ps " exercise for people who want to become better fighters" - surely THAT is a red flag?
It's a bit like those people who feel that screaming is good stress relief so standing around in a park screaming is OK..... If I come across someone screaming for no apparent reason in the middle of nowhere....sorry, my personal safety instinct kicks in!!!
BTW , I have a mate who does track maintenance an a motorbike. He carries a machete and chainsaw. We've had the discussion about how disturbing that looks.