The clear legal authority for actions sanctioned by the United Nations Security Council lies within the United Nations Participation Act.
Title 22, Section 7, § 287d. Use of armed forces; limitationsThe President is authorized to negotiate a special agreement or agreements with the Security Council which shall be subject to the approval of the Congress by appropriate Act or joint resolution, providing for the numbers and types of armed forces, their degree of readiness and general location, and the nature of facilities and assistance, including rights of passage, to be made available to the Security Council on its call for the purpose of maintaining international peace and security in accordance with article 43 of said Charter. The President shall not be deemed to require the authorization of the Congress to make available to the Security Council on its call in order to take action under article 42 of said Charter and pursuant to such special agreement or agreements the armed forces, facilities, or assistance provided for therein...
I had actually never heard of the United Nations Participation Act before this, but it's U.S. Code now. It's Law.
Suffice it to say that this is only a matter of the legality of the attacks on Libya, not about whether you think they're right or wrong. There's a clear argument to be made against these attacks, and its one that I'm not only willing to hear it, I may even agree with...a little.
But as far as Kucinich's statement that this is an impeachable offense, that notion seems to be complete and utter nonsense.