Can a Barbarian stay in rage while polymorphed? [duplicate]

If a raging Barbarian gets polymorphed into a Tyrannosaurus Rex or a Mammoth or something, to give it more hp, does the rage drop? Polymorph says:

The creature is limited in the Actions it can perform by the Nature of its new form, and it can’t speak, cast Spells, or take any other action that requires hands or Speech.

The Barbarian has already taken the rage bonus action. Rage says the following:

Your rage lasts for 1 minute. It ends early if you are knocked unconscious or if your turn ends and you haven’t attacked a hostile creature since your last turn or taken damage since then. You can also end your rage on your turn as a bonus action.

This says nothing about the rage ending if you change shape. So would this work?