In a manner characterized by convulsions; with violent, uncontrollable shaking or jerking movements.
From convulsed (adjective) plus the adverb suffix -ly, creating a word that describes how an action is performed with convulsive movement.
Adding -ly to adjectives to make adverbs is such a common pattern in English that we barely notice it—but 'convulsedly' is wonderfully evocative, painting a picture of uncontrolled violent motion!
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