No, his character changes dramatically throughout the story. Note how he is in the beginning with Gandalf and how he is affected by the ring while with Sam. And by the end he has gone through a significant transformation and is not the same character.
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There isn't really a static character in Stormbreaker as its the first book everybody changes quite a lot.
Annabeth
I would say that she is a dynamic character because she becomes more confident as the movie goes on.
There is no character named Poppin in the Lord of the Rings, however there is a character named Pippin. He is a hobbit, and a friend and traveling partner of Frodo when he tries to destroy the 'One Ring to Rule Them All'.
I think his personality actually changes. In the beginning, he's just a normal young hobbit. Then he gets the Ring, it screws up his life, and he becomes emo. Think about it; it's totally true.