There is a lot of misinformation going around the social media space about whether President Obama (who resisted being pulled into this Libyan conflict), is legally allowed to commit U.S. Military forces to the conflict without the authorization of the United States Congress. 

While I would welcome any input that corrects my understanding, it is currently that he is absolutely and unambiguously allowed to do so.  Why? Because of our well over half-century old agreement with the United Nations which requires such a commitment of armed forces from its Member nations when requested by the Security Council under Chapter XVII of its charter. While a number of pertinent Articles exist in that chapter, the meat and potatoes of the chapter, insofar as Member's armed forces are concerned, is this one:

Chapter VII, Article 42 reads (in its entirety):

Should the Security Council consider that measures provided for in Article 41 would be inadequate or have proved to be inadequate, it may take such action by air, sea, or land forces as may be necessary to maintain or restore international peace and security. Such action may include demonstrations, blockade, and other operations by air, sea, or land forces of Members of the United Nations.

Source: United Nations Charter

Basically, this says that if the non-military efforts of the previous Article (41) are ineffective or not viable, the Security Council may ask its members for additional armed forces to perform whatever military actions or operations its commanders deem necessary to secure peace and security or restore order under the dictates of the resolution.

Now the UN charter's Article 43 also requires that each Member nation ratify this mandate according to their constitutional processes. This has been done by an action of U.S. Congress, and is reflected in:

Use of armed forces; limitations — The 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: Provided, That, except as authorized in section 287d–1 of this title, nothing herein contained shall be construed as an authorization to the President by the Congress to make available to the Security Council for such purpose armed forces, facilities, or assistance in addition to the forces, facilities, and assistance provided for in such special agreement or agreements.

Source: Cornell School of Law

In Conclusion

You can argue about how far the United States might or should go in complying with United Nations' resolutions, and that's a valid argument to have.  Conservatives, isolationists and libertarians have been making it for years. 

You might also argue that the U.S. Constitution, under Article 1, Section 8 grants congress the exclusive right to make war. But subsequent law, embodied in Title 22 above, obviously override this with respect to treaties and agreements already signed into law (i.e. the UN charter).  And even if that were not so, the complexities of the modern era, International Law, the War Powers Resolution of 1973, all suggest that we've had to push the working definitions of "war" and "authorization" a bit. 

It might behoove us—after we dispatch the right wing coup that currently threatens our nation—to amend the constitution, or otherwise clarify these murky issues so that future generations are not constantly preoccupied with their complex and arcane legalities, each and every time the use of military force should arise.

Related

• United Nations' Persian Gulf Resolution, which did NOT specifically stipulate call its members under UN Chapter VII (above), and thus, Congressional approval WAS required for U.S. Military action
• United Nations'_Security_Council_Resolution_1441, authorizing the disarmament of Iraq, where again, Chapter VII (above) was not invoked, and thus, U.S. Congressional approval once again, WAS required.  (This was the famous "Use of Force" resolution that so many Democrats joined Republicans in signing, which was and remains a massive disappointment to the left (and this author) to this very day.