There are three main reasons for European Exploration. Them being for the sake of their economy, religion and glory. They wanted to improve their economy for instance by acquiring more spices, gold, and better and faster trading routes. Also, they really believed in the need to spread their religion, Christianity.
Generally speaking, it would be a "Joint Command" that has line authority to oversee the management of multiple incidents being handled by separate Incident Command organizations, since in this case different agencies are "joined" together.
The best reason the United States might aid another country is to protect US interests abroad, especially when a democratic country is at risk of falling to a non-democratic one, since it is in the US's best interest for foreign nations to be democratic rather than authoritarian. <span />