Submitted themselves - נתנו יד תחת שלמה nathenu yad tachath Shelomoh. "They gave the hand under Solomon;" they swore fealty to him. We have already seen that putting the hand under the thigh (super sectionem circumcisionis) was the form of taking an oath. See the note on Genesis 24:9.

all the princes

1 Chronicles 22:17 David also commanded all the princes of Israel to help Solomon his son, saying,

1 Chronicles 28:21 And, behold, the courses of the priests and the Levites, even they shall be with you for all the service of the house of God...

all the sons

1 Chronicles 2:3-9 The sons of Judah; Er, and Onan, and Shelah: which three were born to him of the daughter of Shua the Canaanitess. And Er...

1 Kings 1:50-53 And Adonijah feared because of Solomon, and arose, and went, and caught hold on the horns of the altar...

1 Kings 2:24,25 Now therefore, as the LORD lives, which has established me, and set me on the throne of David my father, and who has made me an house...

submitted themselves unto [heb] gave the hand under

Genesis 24:2 And Abraham said to his oldest servant of his house, that ruled over all that he had, Put, I pray you, your hand under my thigh:

Genesis 47:29 And the time drew near that Israel must die: and he called his son Joseph, and said to him, If now I have found grace in your sight...

2 Chronicles 30:8 Now be you not stiff necked, as your fathers were, but yield yourselves to the LORD, and enter into his sanctuary...

Ezekiel 17:18 Seeing he despised the oath by breaking the covenant, when, see, he had given his hand, and has done all these things...

Concerning Salutations and Recreations, &C.
Concerning Salutations and Recreations, &c. [1273] Seeing the chief end of all religion is to redeem men from the spirit and vain conversation of this world and to lead into inward communion with God, before whom if we fear always we are accounted happy; therefore all the vain customs and habits thereof, both in word and deed, are to be rejected and forsaken by those who come to this fear; such as taking off the hat to a man, the bowings and cringings of the body, and such other salutations of that …
Robert Barclay—Theses Theologicae and An Apology for the True Christian Divinity