Generalized coordinate

Okay, kiddo! So let's say you want to describe where something is. You can say, "It's there" or "It's over here," but those descriptions aren't very specific, are they? So if we want to be more specific, we use something called coordinates.

Coordinates are like a treasure map that tells you exactly where things are. For example, when you play hide-and-seek, you might say, "I'm hiding behind the big tree by the swings." That's using coordinates to describe where you are hiding.

But sometimes just using normal coordinates isn't enough. Sometimes we need to use something called generalized coordinates. These are coordinates that don't just show where something is, but also how it is moving or changing over time.

For example, imagine a toy car that can move forward and backward, but also turn left and right. If we wanted to describe where the car is at any moment in time, we might use two coordinates: one to describe how far forward or backward it is, and another one to describe how far left or right it is. These are called "ordinary" coordinates.

But if we wanted to describe how the car is moving over time - like if we wanted to draw a map of its path - we would need to use generalized coordinates. These might include things like the car's speed, its direction, and how much it is turning. By using generalized coordinates, we can create a more complete picture of what the car is doing.

So in summary, kiddo, a generalized coordinate is a coordinate that helps us describe not only where something is, but also how it is moving or changing over time. It's like a treasure map that not only shows where the treasure is, but also how it got there and where it's going next!