Mathematical model of Newton's first law

[fedecolo]

Please allow me to get forward, as I feel that your thought is in the right direction.

Newton is a great compilator, but he was an hawful guy. All people around him detested him. He finished his life away of every one, stuck by alchemy and horoscopes, far from science. The famous $1/r^2$ gravitation law has been stated by Robert Hook, referencing the works of Huygens on the sling physics, in a letter to Newton. This last insulted him, saying that he was a freak and did not deserve any attention. But this made the reputation of Newton, the thief, in the "Principia", until us.

A particular experience is the debate with Emilie Du Chatelet about the kinetic energy, and this is a point close to your concerns. Emily shew experimentally that it is $mv^2$ and not $m v$ as Newton postulated (once again, postulate, postulate). Emily was right, Newton was wrong.

In the XIXth century, Lagrange entered in the same mood as yours. He felt that all these postulates should be explanable by the mathematics, in a way or an other. He wrote one of the most important piece of science of the humanity in "Mécanique Analytique", and bound everything and every one (Hyugens, Hook, Newton, Du Chatelet, ...) however by including the Maupertuis's postulate of least action. You heard of Hamilton, of course, but know trom now that this is only a rewrite of Lagrange's work in a particular mathematical way.

I really insist on this : read Lev Landau and Evgueny Lifchitz, Mechanics, Ed. Mir, Moscow. If you need to understand what the classical physics is, you will find no better way. All I told you here is mathematically stated in an elegant mathematical way by these authors.

Your questioning is at the door of the understanding, please get on.

Thank you very much, I'm going to read this book immediately!

 

[A Lazy Shisno]

A particular experience is the debate with Emilie Du Chatelet about the kinetic energy, and this is a point close to your concerns. Emily shew experimentally that it is $mv^2$ and not $m v$ as Newton postulated (once again, postulate, postulate). Emily was right, Newton was wrong.

Eh, you've got a few misconceptions there. First, Newton didn't claim that kinetic energy itself was given by $mv$; in fact, there was no distinction between kinetic energy and momentum during that time. It was Gottfried Leibniz who, as early as 1686, suggested that kinetic energy (which he called vis viva, or "living force") was proportional to the square of velocity. However, this view was widely contested by followers of Newton and DesCartes as it did not seem to be compatible with conservation of momentum, while $mv$ was (again there was no distinction between KE and momentum at the time).

It wasn't until 1719 and 1722 when Giovanni Poleni and Williem 's Gravesande independently confirmed Leibniz's quadratic relationship, empirically, by dropping balls onto clay. Williem 's Gravesande then told Emilie about his findings, who repeated the experiment, confirmed it, then published the results.