This hardly matters, as any single force vector acting upon the free-floating object past the CoG will cancel itself out if applied long enough.
ROFL WHAT?!
Do you even physics bro?
Nothing suggests a starship still couldn't turn on a dime, literally
Other than, you know, Newton's Third Law, which tells us that every action has an equal and opposite reaction. Without a counteracting force to balance the reaction on the opposite side, the reaction
is the entire ship translating as it turns. There's a rotational moment that depends on where the center of gravity is relative to the vector of thrust; the farther the vector is from the center, the more the ship rotates.
This is not the case for starfleet vessels, which appear to locate their impulse engines as close as possible to their center of mass. The Enterprise A, B, C and D all have engines that are either at or very close to their exact center of gravity with RCS thrusters very far from it. Even the Klingon bird of prey keeps a set of impulse engines in a recessed housing aft of the ship, deliberately brining the engines CLOSER to its center of gravity than it should be. This is not something you do if you're planning on using thrust vectoring for attitude control.
Except in this case it isn't - you yourself argued that 180 degrees is being applied in "Relics". Azipods also do the full 360 degrees easily enough.
The
TF-39 jet engine is
also capable of 180 degree reverse thrust. It's not an Azipod, though, and cannot achieve any angles OTHER than forward and reverse.
Which is less than 180. The damning fault is that an RCS thruster involves a flame shooting out.
No, an RCS thruster involves a high velocity jet of reactant mass leaving the ship. This jet may or may not be superheated as a way of increasing its velocity (as is the case for impulse engines). Cold gas thrusters, ion thrusters and particle beam thrusters do not use a "flame shooting out."
Neither do RCS thrusters on Star Trek, with the very notable exception of the enormous thrusters on the reboot Enterprise that are likely more powerful than most ships' impulse engines.
Quite to the opposite, whenever you want to reorient your Trek starship for any practical deep space purpose (setting a heading for Alpha Beta, dodging the Klingon torpedo, getting through the maw of the Space Worm in time), you want maximum delta-vee to go with it
Which is a different issue from pinpoint maneuvering, and why I keep drawing the distinction between thrust vectoring used in course corrections (as it is currently used for launch vehicles and long-burn upper stages that have to make many corrections for the duration of a maneuver) and pinpoint maneuvering, such as reorienting the ship in space along its orbital path, controlling pitch yaw and roll during low-speed maneuvers, aligning the front of the ship with a safe exit corridor (in the case of leaving a space station, maneuvering through a debris field or engaging warp engines for the first time) or maneuvering the ship through space in close proximity to other ships, shuttles or installations.
Pinpoint maneuvering, in other words, is something you do when you want to turn the ship but don't want to go anywhere (yet). Thrust vectoring is inappropriate for that type of maneuver, because the motion of your vessel is more difficult to control and requires a lot more open space than would usually be safe.
They just happen to lie on the aft face (or the top face, or something in between) of the ship, but far, far away from any thrust axis.
They lie on the aft face 100% of the time. Also, you don't actually know what the thrust axis is since you don't know how those ships are ballasted or why. I do not, however, think it is a coincidence that the impulse engines are almost never above the level of the bridge or main habitable structures. It probably has to do with the ship's artificial gravity field; it's likely that objects ABOVE grav plating have a lot more inertia (with respect to the engines) than objects below them.
Rocket flames (no matter how invisible) shooting out from nozzles is something we can categorically rule out as a principle of impulse engine operations.
Or we COULD have until Preemptive Strike gave us this:
"The Enterprise shields have a weak point. When the ship is at impulse,
the thrust destabilizes the shield configuration right at this point. I'm going to try to punch through there."
Obviously not "flames" but it's some kind of ionized gas emitted from the engines to produce thrust.
you yourself argue that reverse thrust is taking place in "Relics", and that can't involve any flames or nozzles since no forward-facing ones exist on the E-D and she never turned around.
And yet the TF-39 jet engine is also capable of reverse thrust, despite never emitting "flames" and the C-5 galaxy never turning around.
I'm beginning to think you're not being serious...
Why are you mixing aerospace engineering into this?
Because aerospace engineering, unlike your conjectures, takes actual data into account. Data meaning "things that actually happen in reality." If data is meaningless to you, then you can just make up whatever random shit you like, in which case I don't care what you think.
[1) Why are they visible "on occasion"?
Because RCS thrusters do not produce "flames." Even in the REAL WORLD this has basically never been the case. Hydrazine thrusters produce a hot gas that is not actually incandescent and is only visible under certain lighting conditions. Cold gas thrusters don't even produce that much, and are visible even less often. Pulsed plasma thrusters will glow near their center but their emissions are never visible at all.
Background sources all describe RCS thrusters as some sort of "particle beam" which is, obviously, something entirely different from "flames". You should no more expect them to be "visible" than you should expect a radar sweep to leave a pale green glow on everything in touches.
2) Why do they require special commands "on occasion" in order to be brought to play?
Same reason they require ANY command on the bridge: for the sake of clarity and to avoid potentially deadly misunderstandings. For things that don't matter, no commands are required; Kirk can tell Sulu "Set course for Ganymede and then put us in orbit. We're gonna take the shuttle down." Sulu knows where Ganymede is and how to get there, he knows (probably) how fast Kirk wants to get there, he knows what a standard orbit is and what it looks like, and he knows what orientation the ship needs to be in to facilitate a safe shuttle launch. Kirk doesn't have to tell him "thrusters at station-keeping, maintain prograde inertial orientation with the ventral hull at 30 degrees to the horizon." Sulu knows all of this and can be trusted to do it.
OTOH, if you're trying to maneuver around in a tiny little space the size of a walk-in closet or, worse, in the belly of a giant pissed off alien robot starship, you want to be as specific as you possibly can about what you want your helmsman to do.
Naval example: Marco Reimius ordering his sonar officer "Re-verify range to target.
One ping only, please."
3) Why is there a separate control interface dedicated to their operation, untouched by the helmsbeing in normal maneuvering operations?
Actually, the question is, why ISN'T there a control interface for vectoring of the impulse engines on any of the diagrams we've seen? Even in the set design for TMP, there is only a single panel on the helm console that can be used to alter the ship's orientation. We KNOW that they use thrusters for this at least some of the time; we don't know and have no reason to assume they would use impulse engines for this too. We do know that impulse engines can be fired in reverse, but there is nothing whatsoever that implies they can be fired sideways, laterally, oppositionally (for roll control) or fine-tuned for manually-adjusted course corrections. Indeed, the fact that vector exhaust is very difficult to use for that purpose is the probably the whole reason the helm console has a NAVIGATOR in the first place: Sulu can control thrusters and engine output and Ilia has to program the computer with a destination solution which allows it to make those very fine adjustments to the engine exhaust to keep them on course. This, more than anything, explains why Enterprise never has to make midcourse corrections while flying on impulse power, the computer does it in real time.