I recall the 25th Anniversary computer game has recharging banks for the weapons systems, with phasers having a faster recharge than torpedoes. But that was partly just for usefulness in a game context. 
 Scotty also managed to recharge one bank on the Constellation in "Doomsday Machine" so that Kirk had at least something to work with.
Regarding transporters and shuttles, I might have to look through my nerd library just for fun. I sometimes wonder if the systems as shown onscreen in TOS were somewhat simplistic for the crew complement, assuming there's only a few main transporters at best and a limited number of shuttles (which typically only hold 6 crew apiece). Jackill's books tend to give classes a higher ratio of various shuttles and sometimes fighters, depending on the mission profile, with installations like starbases potentially having a lot of small craft support for various functions.
	
		
			
		
		
	
				
			
 Scotty also managed to recharge one bank on the Constellation in "Doomsday Machine" so that Kirk had at least something to work with.Regarding transporters and shuttles, I might have to look through my nerd library just for fun. I sometimes wonder if the systems as shown onscreen in TOS were somewhat simplistic for the crew complement, assuming there's only a few main transporters at best and a limited number of shuttles (which typically only hold 6 crew apiece). Jackill's books tend to give classes a higher ratio of various shuttles and sometimes fighters, depending on the mission profile, with installations like starbases potentially having a lot of small craft support for various functions.
				