The common perception that the stiffness of a machine/tool post is the reason for tool chatter is debunked very early in this video. I science the $%$" out of tool chatter and look at some of the conventional and non-conventional ways to get rid of tool chatter, as well as deal with the elephant in the room.... high frequency chatter when using a small boring tool and/or finishing cuts.
Check out:
https://www.adendorff.co.za/engineering-accessories/lathe-chucks
https://www.adendorff.co.za/engineering-accessories/quick-change-tool-posts
for the quick change and chuck used in this video.