And it turns out that the familiar path - the path exactly predicted by Newton's laws - is the path with the least possible amount of action. These different possible paths will have different actions associated with them. You can imagine different possible paths the ball might take as it's thrown to you. This number is called, for various historical reasons, the action of the object in motion. At the end of the motion, you can add up all those differences and get a single number. If you watch a ball in flight, for example, then at every moment in time, you can calculate that difference. The key is the difference between the kinetic and potential energies of the object in motion. Newton didn't have the answer, but Lagrange did. Newton's insight was his ability to find a general law of motion that could predict the trajectory of that thrown ball.īut why should Newton's laws be correct? Why should a thrown ball follow the familiar path? Why don't balls jump backward first, or shoot off to Mars on their way to you? Why does the same path happen every single time? In other words, why do objects behave the way they do, rather than any other way? The universe could have chosen literally any behavior for thrown balls or any other objects in motion. You can do this because in your lifetime, you've seen lots of balls thrown at you, and your brain has deciphered that thrown objects follow a rather common set of trajectories. If I were to throw a ball at you, you would probably have a decent chance of catching it. Specifically, Lagrange found that the difference between an object's kinetic energy and potential energy unlocked something deeply profound about the universe. He found that by looking at the kinetic and potential energies of an object, he could also derive his own laws of motion. Newton found that the combination of mass, acceleration and force was very powerful indeed, allowing him to formulate his famous Force = mass * acceleration equation as a fundamental law of the universe.Ībout 150 years after Newton developed his laws of motion, another mathematician, physicist and all-around genius, Joseph Louis Lagrange, developed his own formulations. Some of these properties may be very useful in predicting the ball's future motion, and some less so. That ball has a lot of properties that we might find useful - things like its position, velocity, acceleration and mass. Think about a ball being thrown in the air. But examining forces and masses isn't the only way to describe the world around us.
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