the general principles of bird flight, you might want to start with
our Bird Flight Primer.
It takes a lot of energy to flap such large wings, just like it's a lot of work running with a large kite until it takes off! Two scientists who studied eagles, Jon. M. Gerrard and Gary R. Bortolotti, write that "Eagles are capable of sustained flapping flight but they usually spend little time doing it. During the month when Cindy (one of the female eagles they studied) was observed intensively, she averaged less than 2 minutes per hour in flapping flight. That is not surprising when one considers the large expenditure of energy required by the pectoral and supracoracoid muscles to power the huge wings. The energy needed to maintain a bird in flat soaring or gliding flight is much less, perhaps a 20th or less the power needed for flapping. Therefore, eagles will always choose to soar or glide when possible."
That is why when eagles are flying long distances, especially on migration, they often soar on thermals until they reach a great altitude, and then use the gliding/soaring method of flying to cover the longest distance using the smallest amount of energy.