Verlet integration

Okay, imagine you are playing with a ball. You throw it up in the air and it comes back down. Verlet integration is like a way to figure out where the ball will be at different times without actually having to watch it go up and down.

Here's how it works:

First, we need to know the ball's position and speed (or how fast it's going) at one moment. Let's say we know it's at the height of 5 and it's going 2 meters per second.

Then, we use some fancy math to figure out where the ball will be at the next moment. We take the ball's current position and add its speed multiplied by time. So if we want to know where the ball will be after 1 second, we take 5 (the current position) and add 2 (the speed) times 1 (the time). That gives us 7, which means the ball will be at the height of 7 after 1 second.

But wait, there's more! We can also use verlet integration to figure out where the ball will be after more than one moment. We just keep doing the same math over and over again. We use the ball's new position and its old position to figure out its speed, and then we use that speed to figure out where it will be at the next moment.

And that's verlet integration! It's a way to predict where something will be at different times based on where it is now and how fast it's moving.