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fixed the stability thing I was confused about.
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user21103
user21103

As just one example consider the Lunar landing. This is done by having the LEM sit If you think about a vehicle sitting on top of its enginea rocket, which is initially slowing it down and then later transitioning into keeping it up. The engine is atwith the bottomthrust vector of the LEM for obvious reasons, and if you think about itrocket passing through the centre of mass of the system for a moment you'll realise that a system like that isn'tit's not stable: there's nothing making it wantswant to fall overpoint in any particular direction. Try resting something on But you need it to face in some very particular direction so that the tiprocket's thrust both points the way you want and the vector passes through the centre of a pencil to see this. You'd likemass of the thing not to fall over, and not onlysystem so it's not to fall over butexerting a torque on it. And you need it to follow a very careful trajectory down to the surface which means the thrust direction has to be continually controlled as does the amount of thrust: it has to reach the surface with fuel left, travelling very slowly, and in the right place. They have just enough fuel to do this because lifting fuel to the Moon is extremely expensive.

And they need to do this every second or so. Oh, and did I mention that while all this is happening they need to be stoppingmake sure the LEM falling over, since it's not stable,vehicle remains pointing in the right direction which is it's own horrible computational problem? And while doing that they need to watch the instruments to check nothing bad is happening, make abort decisions and so on and so on.

As just one example consider the Lunar landing. This is done by having the LEM sit on top of its engine, which is initially slowing it down and then later transitioning into keeping it up. The engine is at the bottom of the LEM for obvious reasons, and if you think about it for a moment you'll realise that a system like that isn't stable: it wants to fall over. Try resting something on the tip of a pencil to see this. You'd like the thing not to fall over, and not only not to fall over but to follow a very careful trajectory down to the surface: it has to reach the surface with fuel left, travelling very slowly, and in the right place. They have just enough fuel to do this because lifting fuel to the Moon is extremely expensive.

And they need to do this every second or so. Oh, and did I mention that while all this is happening they need to be stopping the LEM falling over, since it's not stable, which is it's own horrible computational problem? And while doing that they need to watch the instruments to check nothing bad is happening, make abort decisions and so on and so on.

As just one example consider the Lunar landing. If you think about a vehicle sitting on top of a rocket, with the thrust vector of the rocket passing through the centre of mass of the system for a moment you'll realise that it's not stable: there's nothing making it want to point in any particular direction. But you need it to face in some very particular direction so that the rocket's thrust both points the way you want and the vector passes through the centre of mass of the system so it's not exerting a torque on it. And you need it to follow a very careful trajectory down to the surface which means the thrust direction has to be continually controlled as does the amount of thrust: it has to reach the surface with fuel left, travelling very slowly, and in the right place. They have just enough fuel to do this because lifting fuel to the Moon is extremely expensive.

And they need to do this every second or so. Oh, and did I mention that while all this is happening they need to make sure the vehicle remains pointing in the right direction which is it's own horrible computational problem? And while doing that they need to watch the instruments to check nothing bad is happening, make abort decisions and so on and so on.

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user21103
user21103

As just one example consider the Lunar landing. This is done by having the LEM sit on top of its engine, which is initially slowing it down and then later transitioning into keeping it up. The engine is at the bottom of the LEM for obvious reasons, and if you think about it for a moment you'll realise that a system like that isn't stable: it wants to fall over. Try resting something on the tip of a pencil to see this. You'd like the thing not to fall over, and not only not to fall over but to follow a very careful trajectory down to the surface: it has to reach the surface with fuel left, travelling very slowly, and in the right place. They have just enough fuel to do this because lifting fuel to the Moon is extremely expensive.

The astronauts have a couple of tiny windows out of which they can see. In the initial phase of the descent those windows are facing away from the surface: they can't see the surface at all. Because the LEM is under acceleration the whole way down 'down' in the LEM is not in fact down, so they don't know which way is up most of the time. So they're going to have to do this all by instruments.

Well, what can instruments tell them? They can know which way the LEM is oriented in inertial space. They can know how far it is above whatever happens to be on the surface below them (so: not how far it is above the landing site, but how far it is above whatever mountain they are passing over). They can't know its position in the two other axes really. They can know the acceleration vector of the LEM in its own frame. And let's say they knew both the position and the velocity at the start of the descent.

So what they need to do is to work out where the LEM is, and how fast it is moving. To do this they need to:

  • rotate the acceleration vector they have in the LEM's frame to one in the platform's frame, which involves trigonometry;
  • rotate this further into the appropriate coordinates for the Moon's frame (which depends on their calculated horizontal position);
  • integrate the horizontal component, once to get horizontal velocity and then again to get horizontal position;
  • integrate the vertical component once to get vertical velocity;
  • integrate it again to get computed vertical position, compare this with the readings from the radar and, I guess, some kind of terrain map to check it all makes sense;
  • compute where they are with respect to where they should be;
  • compute the thrust vector they need from all this, rotating it all back into the LEM's frame.

And they need to do this every second or so. Oh, and did I mention that while all this is happening they need to be stopping the LEM falling over, since it's not stable, which is it's own horrible computational problem? And while doing that they need to watch the instruments to check nothing bad is happening, make abort decisions and so on and so on.

This is so far beyond the capabilities of a human as to be hard to describe. This is just one of the reasons why all rockets use computers for guidance: the problem is too hard to solve without one. The V-2 used a computer, for instance – it was an analogue computer, but it was a computer.