http://legal-dictionary.thefreedictionary.com/declaration+of+war
Not the most scholarly of sources but I hope this suffices. From what it's worth it claims to be from:
"A Law Dictionary, Adapted to the Constitution and Laws of the United States. By John Bouvier. Published 1856."
So I hope this works for ya. On to the show:
"DECLARATION OF WAR. An act of the national legislature, in which a state of war is declared to exist between the United States and some other nation.
2. This power is vested in congress by the constitution, art. 1, s. 8. There is no form or ceremony necessary, except the passage of the act. A manifesto, stating the causes of the war, is usually published, but war exists as soon as the act takes effect. It was formerly usual to precede hostilities by a public declaration communicated to the enemy, and to send a herald to demand satisfaction. Potter, Antiquities of Greece, b. 3, c. 7; Dig. 49, 15, 24. But that is not the practice of modern times. In some countries, as England, the, power of declaring war is vested in the king, but he has no power to raise men or money to carry it on, which renders the right almost nugatory.
4. The public proclamation of the government of a state, by which it declares itself to be at war with a foreign power, which is named, and which forbids all and every one to aid or assist the common enemy, is also called a declaration of war."
So essentially a declaration of war is an authorization for acts of war. This authorization, as noted in the Constitution, is only able to be granted by Congress. Thus the only Constitutional authorization for acts of war is that which is granted by Congress.
Now, it should be noted that defense of the country is allowed without Congressional approval. The President as Commander in Chief is tasked with defense of the country from imminent attack and does not need authorization to execute that responsibility. (I don't have the specific clause handy but I recall the President explicitly being given this authority; hence the change from "make" to "declare.") However, for anything beyond the scope of an imminent attack from a country posing a direct threat to the US, the authorization must come from Congress. In the case of Libya it never did and likely never will.
So I'm going to have to respectfully disagree with the idea that the President can authorize use of military force wherever and whenever he desires.