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Assuming spacecraft are using contemporary propulsion technology, and are engaging in a dogfight in outer space (whether they are manned, drone, or autonomous), would the movements of the craft be abrupt and jerky, or smooth and graceful?

To expand on Cort's comment. Propulsion in space is too costly and distances too great for a dogfight to happen. With modern tech, space combat is limited to more of an artillery duel between satellites that are on more or less fixed trajectories. If they start trying to move around too much they are going to just end up falling into the atmosphere or flying out into space. They can also see eachother way too clearly to ever survive long enough to get into dogfighting range even if they tried. Your armed satellites may have some maneuvering jets designed to make subtle course corrections for dodging, but high speed evasions would use too much fuel and need too heavy of thrusters to be an effective war doctrine using rocket propulsion.

So to answer your question... they would be "smooth and graceful" in the since that they will not actually be moving around much to begin with.

Perhaps one day we will have some manner of technology that will make orbital mechanics and rocket equations a moot point in the face of overwhelmingly efficient and powerful propulsion systems, with what we've got today. Just getting into a stable orbit is a trick unto itself.

There won't be any dogfights in space without the science-fiction tag.

The reason is that we have been toying with lasers for a long time. The YAL-1 project was cancelled, yes, but it worked kinda well in 2014. If we are going to space, we are going to have better technology. The lack of an atmosphere will also make it much easier to hit stuff with lasers.

YAL-1 could deliver well in the range of 2kWh in 3 to 5 seconds. That is enough to really ruin the day of whomever is in the receiving end - too concentrated and you get holes in our hull, too dispersed and in the very least your instrumentation goes blind.

You just can't compete with lasers. The fastest acceleration we've ever managed for a rocket-powered vessel was with New Horizons. It passed the Moon's orbit within nine hours of its launch. Light, however, is much faster and will cover the same distance in close to 1.3 seconds.

So don't try to enter a dogfight in space - as soon as you are seen, you are toast.

Someone might say "oh come on Renan, this means acceleration will be jerky in order to avoid lasers". The attacker may simply spread the laser wide. As long as you are within the beam you are in trouble, for the same reason that laser pointers are dangerous to aircraft. The laser will not reach you as a small dot. And once you are blind, there isn't much point in doing random maneuvers.

The short answer is jerky and abrupt, but the longer answer is far more interesting...

First of all, the preceding answers explain why fighter combat in space is really a bad idea; it's not an efficient use of propellants or fuels, and you're far better off doing what was done in naval warfare; focusing on a smaller number of larger ships with REALLY big, long range, powerful guns. But if you insist on putting fighters up there, the first thing you have to do is get the idea of air combat out of your head; space fighters and dogfights are going to look completely different.

Let's start with the fighters themselves. They are not going to be sleek, aerodynamic craft that bank and turn gracefully; they're going to be spheres.

The reason for this is very simple. In an atmosphere, the air itself gives the plane something to help the craft bank and turn; the wings effectively push air around themselves and shape it with control surfaces to move the plane in a desired direction; it's actually pushing against the air to go where it needs to go. In space you don't have that so every change in velocity (whether it be speed, direction or both) must be done with a maneuvering thrusters. To make your fighter as agile as possible, you want to be able to thrust in almost every direction so that you can react to the combat around you with a minimum of orientation changes (as these also cost fuel) and to do that, you want thrusters pointing out in almost every possible direction. That means a sphere.

Now, it's possible for you to thrust in almost any direction without a sphere if you have a thruster that can turn and spin around you; say 3 thrusters each at 120^o from each other on a ring that can rotate and spin around your ship, but in a combat situation do you really want to wait the half second or so for your ring to put the thrusters in the right position? Probably not. So, sphere.

Now, dealing with the maneuvers; because you're not pushing against anything but firing a thruster every time you want to turn, and because you don't want to ramp up the thruster gently (time is not your friend in combat) you're going to have a very abrupt, jerky, but agile turning approach. You'll be able to pull off moves that are simply not possible in a plane, and most banking turns a plane uses will actually be inefficient for this kind of fighter, but you're in a different medium to begin with which is why you need to think in a different way as to how you move about in combat.

Realistically; for space fighters, you want them to be drones. The G forces and inertial effects on the craft are not going to be friendly to your pilot, who needs to be able to maintain some consistent frame of reference for 'up' and all the accompanying directions. You can't do that in a space fighter because every thrust is going to act on the pilot to reorient his 'down' to align with the thruster just fired. Also, because of the fact that you're moving in a way that planes can't most of the time, your pilot will suffer massive G-forces and won't last long in the cockpit. Further, not having to maintain life support for the pilot means you can make the craft more compact, making it a smaller target while also allowing it to be more nimble. It's basically a weapons platform surrounded by engines all pointing outwards.

The important thing to note is that cars, planes, and even boats can manage their smooth turns because they're all effectively pushing against something; a road, the ocean, or an atmosphere. Your space fighter has nothing to push against, so it must use its engines to do ALL the pushing. Once you get your head around that, smoothing the change in velocity means making the craft inefficient and before long, you're taking the pilot out of the craft for his or her protection more than anything else as you give your craft an edge (hopefully) over the enemy craft.

Put even more simply, if modern drones could be designed to make instant 90^o turns in the air, they would be simply because it would give them an edge in combat. Your space fighters CAN be designed to do that, so they will.