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Hello. When a missile changes direction over time to reach a line to target, how do you know when to begin turning?

What is the math called? Where might I find examples of this math?

To restate my question:

If your direction vector is due north, and a horizontal line to the target can be drawn from a point 500 meters in front of your nose to the target point at direction vector due west, how do you know when to begin turning?

The change in direction over time is measured in radians (of change in direction) per second. But since we aren't only aiming to change our direction vector toward the target due west, we also have to be on this heading when we reach the target's height (hence I mentioned we have to end up on a line to target) This presents the variables of: our position, our acceleration, our current speed, and our current direction vector. All of these things are known quantities.

Thanks for any help!

What is the math called? Where might I find examples of this math?

To restate my question:

If your direction vector is due north, and a horizontal line to the target can be drawn from a point 500 meters in front of your nose to the target point at direction vector due west, how do you know when to begin turning?

The change in direction over time is measured in radians (of change in direction) per second. But since we aren't only aiming to change our direction vector toward the target due west, we also have to be on this heading when we reach the target's height (hence I mentioned we have to end up on a line to target) This presents the variables of: our position, our acceleration, our current speed, and our current direction vector. All of these things are known quantities.

Thanks for any help!

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