[synopeas]

This is a very quick and basic version as I don't have much time.

Play the video & search for a file with url starting with "http://www.youtube.com/api/manifest/hls_variant/key/yt1/ip/"

Open that file in a text editor and you will see a list of 6 streams of different resolution. Pick the best, or fastest your bandwidth can handle, and put it in this template in place of the part between inverted commas:-

ffmpeg -i "http://www.youtube.com/api/manifest/hls_playlist/id/.../file/index.m3u8" -c copy seg.ts

If you use that command ffmpeg will download the stream as it is, combining the segments. You can worry about editing the file, or converting it later.