I know that the "normal", not the later big wing B-57 used a starter cartridge. Looked kind of like an oil filter and mounted in the front of the engine in that streamlined housed. Pretty much hit the switch, it burned providing the pressure to start the engine rotating. The mechs said you had to clean where starter cartridge mounted, where the hot burning gases went on into the engine, if not after a few starts the crud would build up and the little bullet fairing and the starter would blow off the engine, not a good thing. Clouds of black smoke coming out of the side of the engine on a normal start. Really impressive. The engines were old Buick engines from F-84s but I don't know what they did to them to put them on the B-57. So I don't kow if you could start anything else that way, I would guess you could. We used to have an old air start unit at Cal Poly, seemed to have two or more V-8s for power, pretty impressive when they got them going and all reved up. Loud in the way that a bunch of teenagers loved!
I've got a little jet and turbo prop time. Pretty much each basic engine type starts the way you are told to start it, PT-6, PW-118 and so on, each engine family. All the turbo props I have flown have used starter generators. Flip the switch to start and it drives the the compressor section and all that. Most of them also start the ignitors, you hear a snapping noise most the time. When you get the right rpm (ususally in %) you add fuel, can be a cut off lever, a low pressure fuel shut off, a condition lever or some other name. If all goes well the fuel lights off, you get rapid rise in the engine temp (egt most common) at the right rpm the starter becomes a generator. The ignitors stop snapping and all is right in your world. Check temps and pressures. Some you have to flip a switch to reset/select generator. If the starter does not drop off line (quit being starter) you have a problem. Not good. Go into checklists and if you can't get it out of being a starter the aircraft I have flown tell you to shut the engine down, don't go flying and call the mechs. This wasn't me, had friend ignore the starter engaged light one time and at the next airport they found the starter on the bottom of the engine cowling... I would have thought he might have noted either a hydraulic pump or a generator off line?? What was his FO doing? Sleeping? ONLY ONE person at a time should sleep in a two person cockpit! We had the time to walk over and see that starter and some pissed off mechs.
Stopping the engine you usually use the same lever to starve the engine of fuel. I have had that not work and have to pull the firewall shut off valve also called the e-handle on some and that should stop air, fuel, and hydraulics at the firewall. At idle it takes a while before it does shut down. Got to burn all the fuel in the lines ahead of the firewall. You need some power to start, some smaller aircraft you can use the battery, on larger ones the battery doesn't have enough power. A couple of aircraft I flew you had at best two APU start attempts without external or ground power. The APU is a small jet engine that you can get bleed air for air conditioning and electrical power, in these type aircraft, in the bigger aircraft used for your powerplant starting, airconditioning, and by electrically driven hydraulic pumps hydraulic pressure. I flew one four engine airplane that had three generators, the APU, the (if I remember right) and the outboard engines, the inboards had the hydraulic pumps. At the gate you want to use ground power, either the jetway or a ground power trailer, you don't want to use the main engines and most airports restrict APU use these days, they are loud! Air, when you can get it for the airconditioning is great and a lot of even smaller aircraft do have an airconditioning inlet for ground airconditioning.
Most bigger airplanes have an ADG or a variation of it, Air Driven Generator, sometime called a RAT for ram air turbine, it drops out when you tell it to and it has blades that should spin and provide electical power, on ours you can select it to send ALL that power to a hydraulic pump so you can get a little electrical power or a little hydraulic power... you either power part of one main bus or get some hydraulic power to a few items. To be honest if you are down to having to choose between using the ADG to give you one or the other and you have NO other hydraulics or electrical power...it really wasn't your day to go flying! Works to about 80 knots in the book but we saw it still giving us stuff at 60 knots and then the FE got busy and didn't really note when it wasn't doing anything. Some noise, you know it is out but not all that bad.
Oh, and if the engines are hot, then you have to worry about the temp in the engine before the start (the hotter it is before start the hotter start you get and if it gets too hot you HAVE to abort the start and there is risk damage. (We were told that most of the wear on a turbine engine that effects its life is during the heat rise in the start cycle so you try for cool starts and to avoid wasted starts and hot starts both the temp getting too hot and the engine being hot right before you start.) So you might risk doing cooling cycle, like a start but you have the ignitors off and don't add fuel. The ambient air flowing thru should drop the temp inside. Or you just might let it spin a little longer, get a little more air going thru it and the temp should start going down. You might have a starter limit, starter engaged time and how many stgarts during a time period...most the ones I have seen limit you to three starts and then you sit for a while. I once got stuck in SFO with a limit that said we had to let the starter cool to "Ambient". I'm going to open the engine to feel the starter before trying another start? Who thought of that one? Is that an hour, two hours? What OFIDSUJFIO thought that one up! One of the few times I really lost it, I was pissed! To throw a few bags that could have gone on the next flight...which due to our delay beat us there! Big delay pissed pax and a longer day that we already had and it was long!
Add the fuel too soon, too low of RPM, POOF! real hot start or if the ignitors are not snapping or all sorts of things can go wrong. I've seen several feet of flame coming out from a bad start. As long as it doesn't overtemp...okay but it does scare the pax. Also seen windows melted, again, I have done plenty of stupid things in aircraft but have yet to melt a window.
And yes, you DO want hydraulic pressure, they tell you that the accumulators will give you 10, 15, 20, 25 brake applications...don't believe them. I know a guy that ran over several Cessnas at KSMF nine applications into a supposed 25? Me, I shut an airplane down blocking a runway at KSFO once when we lost nose wheel steering and dumped most of our hydraulic fluid on the ground. No brakes...no nose wheel steering. I no drive! I shut down, waited for Maintence to come get "their" airplane. I didn't want that one anymore! (At first they were a bit pissed at me for refusing to taxi back to the gate but after they got there and really looked at it...they didn't want to taxi it either...LOL)
Jets: The smaller jets I have flow were pretty much like the turbo-props in starting and stopping. Big ones for the most part use compressed air, best source is the APU, ground air can work but at times we have needed TWO carts to get us enough air to start. Not all that much PSI but the flow is big. Not always can you get two air units (huffers) at a time and you still need the electrical power for all the other stuff. So now you have three carts plugged in and the meter is running and you HAVE to start one engine in the gate (some places will not allow that at all other you can work with) or arrange for a long push (Ground will really love you for this mess) get the carts plugged in while you sit blocking the taxiway or alley, the checklists done, and you are doing something not usual so you are going slow and really reading them and other people want to push or get into their gate...you feel the LOVE! Get the carts unplugged once you get one running...and you are in East BumXXX and they don't understand English all that well and you are just haveing a wonderful day and you have about six hours more to go, ten hours into the day and you were supposed to be on short final to your overnight spot right now...your fun meter is pegged! Parts of Africa they might not have diesel for the tug and GPU's. Been there done that, it isn't all that fun!
We like AC but we can use DC and it depends upon the aircraft. With luck we have one shot at getting the APU going with the battery. In DC-10s and 11's you can run #2, the tail engine and use it as a big APU, not the best choice, noise, fuel, the jet blast. But if you are doing a turn in East BumXXXX and there is NO working ground power or GPUs and your APU is broken well you don't want to spend the night (and a broken airplane in some parts of the world can turn into days there...(we carry almost $2,000,000 (no, I don't know if that is retail or wholesale) of parts and a mech with us most the time) there now do you? So yeah I have done that. Someone that is qualified HAS to be on the flight deck since there is NO auto shutdown on the engines, most APU's have lots of reasons to auto shutdown so someone being on the flight deck isn't so important. Oh, and since dispatch didn't figure that into their fuel load you got to guess how much that is going to burn and hope you have enough fuel to meet the dispatch fuel requirment but not make you overweight for takeoff or landing. You don't want to dump fuel...unless you really have to so you might fly slow with some drag out to get you to landing weight if you really have to. Oh and of course you can't dump fuel in the gate so you have to get defueled and not all trucks can do that and some airports consider defueled fuel to be junk and not to be put back into another airplane...oh, and they don't give you any money for it either, you bought it soooo sad. You might be talking to your Chief Pilot when you really wanted to be sleeping! "What's this about you off loading 30,000 lbs of fuel....? And you were four hours late leaving.....?"
The short of it is, you start and stop the engines the way they tell you too, and that is also affected by the airport. It would be very unusual to run anything but an APU in the gate and that is getting rare but it does happen but you will still hear fans, possibly the airconditioning packs and even hydraulic pumps as systems are being checked.
The old round engines were wonderful but I knew a guy that had flow the Connies at the end of their international work at TWA and then went into the early 707s back when jet engines were not all that good. In one series of flights on his last trip in the Connie he had something like two shutdowns and two precautionary shutdowns. Never had to shut down turbine engine. I can't make that claim but I do know I picked up a large goose coming out of KRNO one time and didn't shut down the engine, the viberationg was high but in limits (didn't know about the bird strike). Got to our destination, found the bird damage, wrote it up, they gave us another airplane and we left. They pulled the damaged fan blades and the ones 180 degrees away, replaced them (I think in less than an hour including the paperwork) and flew it until that night and then changed the engine. Almost any fool can handle a turbine engine, you needed a real Flight Engineer on the big recips.
The real simple idea to keep in mind that if you have good airflow thru the engine and all the other parts are doing their part, the FCU, ignitors and all that good stuff you should have a cool start. Wind up the tail pipe, spin it up longer or to a higher rpm, hot since you just shut it down, let that cooler ambient air cool it down. Go to "max motoring". Yeah, it can affect seal life if you do it too long on some engines and you cannot run the starter too long but I bet the seals hate hot starts more than most other things.
I like P&W but the only engines I have had to shut down or have quit on me were Pratts. But I trust in P&W.......And GE!