[Avodah] kabbalat hashabbat

[Eli Turkel]

I am looking for sources for the tefillot of kabbalat shabbat
In partuclar mizmor le-dovis seems to be the oldest chapter in
Tehillim connected to kabbalat shabbat.
What is its connection to shabbat?

also why some parts of lecha dodi are not said shabbat yomtov
and parts of the previous tehillim are skipped
(I know of the shiur of RYBS - looking for other reasons)

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Eli Turkel