Greek Hamippoi and Germanic light infantry are noted as fighting in close cooperation with cavalry, even intermixing with them, but not, AFAIK, as hitching a ride.
Thucydides 5.57.2 mentions hamippoi
; oddly, most online translations render this as "dismounted troopers", but this is probably an example of the looseness with which Classicists often render technical terms. Jowett has "five hundred cavalry, and attached to each horseman a foot-soldier", and more literally it says "five hundred cavalry and hamippoi
to the same number", leaving the technical term untranslated. The literal meaning is something like "ones accompanying horses".
Apart from the mentions in the Hellenica, Xenophon has this to say in The Cavalry Commander
Another duty of a cavalry commander is to demonstrate to the city the weakness of cavalry destitute of infantry as compared with cavalry that has infantry attached to it. Further, having got his infantry, a cavalry commander should make use of it. A mounted man being much higher than a man on foot, infantry may be hidden away not only among the cavalry but in the rear as well.
Near as I can make sense of the Greek syntax, he's using hamippoi
here not as a noun, but as an adjective "accompanying horses" (modifying pezoi
"infantrymen"). The implication is surely that the utility of such soldiers was not universally recognized - their use had to be argued for. Given the experience of later ages, I'm inclined to believe that the skeptics had a point and that mixing light infantry with cavalry is not in general very useful. That some Greeks (and Germans) found it helpful would then be due to particular circumstances - one might suggest small horses, unsophisticated horsemanship, and little emphasis on shock action as relevant.
The Constitution of the Athenians (4th century) mentions "the hamippoi
" as part of the military establishment but gives no further details.
The word also occurs in a non-military context in Sophocles' Antigone
That would exhaust the occurrences of the word in Classical literature that I can find via
the Perseus Project.
There is a story about Kublai Khan having infantry hitching a ride with cavalrymen, which would make Yuan another candidate for any battle card to this effect. But only know of this via
wargamer lore, no idea what the original source may be. Nor do I know if it had any battlefield effect that needs representing.
Polybius BTW probably didn't write about velites under that name - he wrote in Greek, and normally used approximate Greek equivalents for Latin technical terms (which sometimes causes ambiguity for us poor moderns).