In English-Japanese dictionaries, they are all defined along the lines of "brave" or "courageous".
Japanese dictionaries describe all of them more or less as "not fearing danger", using a phrase similar to「危険や困難を恐れない」for each of them. Adding to my confusion, they seem to follow a circular logic: the entry for 勇気 uses いさましい; the entry for 勇ましい uses 勇敢; and the entry for 勇敢 uses 勇気.
Of the three, 勇気 seems to be the most common while 勇ましい is by far used the least. On 少納言, 勇気 had almost 25 times as many hits as 勇ましい.
Ignoring grammatical differences (I'm aware of their parts of speech), what is the difference between them? And if they really are close synonyms, how come 勇気 is used so much more than 勇ましい?