Jacobi field

Jacobi field is a lot like a game of follow the leader. Imagine you and your friends are all holding hands and walking in a straight line. Your friend in the front is the leader and everyone else is following behind.

Now, imagine if your friend in the front suddenly veers off to the side. Because everyone is still holding hands, you and your friends would be pulled in that same direction.

In math and physics, a Jacobi field is like those friends being pulled in a different direction. It's a way to measure the difference between two paths in space, when one path starts to veer off in a different direction than the other.

Just like in the game of follow the leader, a Jacobi field is a way to measure how much the direction has changed and how much of a pull it has on the other paths. It's a really useful tool for studying things like gravity and motion in space.