Does Achilles make a cyclical journey in the Iliad?

Well, he gets really angry at Agamemnon and then refused to fight until his friend, Patroclus (sp?) is killed. Then he fights for the Greeks like crazy and ends up dealing the Trojans a terrible blow by killing Hector who was the best Trojan at war. A guess that's a cycle. Being the best fighter and then choosing to not fighting and then fighting again to deal the Trojans a critical blow...