I have no experience with heavy equipment like that but my intuition would tell me not to try moving with the weight attached.
I would work the area to be pounded in an inward spiraling path.
Drop the weight.
Back up the crane.
Tilt crane forward and attach weight weight.
Slowly bring crane with weight vertical.
Raise weight.
Repeat.
At the corners of this square spiral the crane, while free of the weight, would "turn the corner" before picking up the weight again.
This is just my conjecture about what to me is a fascinating problem. Hopefully, some of the folks who do this for a living will chime in and explain how it's really done.
Another fascinating question is why they are pounding the earth at all.
Breaking a surface layer - surely there are ground level machines better suited to doing this.
Compacting the surface - maybe but a cylindrical weight leaves patches uncompacted.
Generating vibrations to map sub-surface layers - sure, but why would they have to move the impact point around in such small increments?
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