History of Newtonian Mechanics?

[ssj5harsh]

I have been wondering how the classical mechanics that I study in my textbook today was framed. Newton gave his laws of motion, but what about vectors, who invented those. We deal with freely falling bodies and acceleration due to gravity while studing kinematics. But I know that the law of gravitation was developed by Newton nearly 40 years after he framed these "laws" of mechanics. He didn't know the value of 'g', 'G', or anything else. How did he work?
Somebody should point me to a proper link or book where I can clarify such useless, irrelevant doubts.
Thank you.

 

[Andrew Mason]

I have been wondering how the classical mechanics that I study in my textbook today was framed. Newton gave his laws of motion, but what about vectors, who invented those. We deal with freely falling bodies and acceleration due to gravity while studing kinematics.

Newton used geometry extensively but did not invent or use vectors. The development of the whole field of vector mathematics has been relatively recent. Most of it occurred in the last half of the 19th century. There were two different approaches: Sir W.R. Hamilton and his 'quaternions' and Hermann Grassmann/J.W. Gibbs. Gibbs wrote the first textbook on vector calculus in 1901 and it forms the basis for most of what is now modern vector calculus.

But I know that the law of gravitation was developed by Newton nearly 40 years after he framed these "laws" of mechanics. He didn't know the value of 'g', 'G', or anything else. How did he work?

I am not sure where you got this information but it is incorrect. The universal law of gravitation was developed by Newton when he was in his early 20's (around 1665) and published in his Principia Mathematica in 1887. He also provided an estimate of G based on an estimate of the density of the Earth and moon. Galileo had measured g so g was well known.

Somebody should point me to a proper link or book where I can clarify such useless, irrelevant doubts.

Crowe, A History of Vector Analysis, 1967. A short essay by Crowe is here:
www.nku.edu/~curtin/crowe_oresme.doc[/URL]

As for Newton: there are numerous sources. eg [url]http://www.blupete.com/Literature/Biographies/Science/Newton.htm[/url]

AM

 

[Amauta2K]

For a more serious study you can go to:

http://dibinst.mit.edu/BURNDY/Collections/Babson/OnlineNewton/Principia.htm

this page has complete and original works of Newton ( well many texts are in latin and french..., i speak spanish so it wasn't too hard to learn enough to read them ). Any way they will show you the original sense of his work.


For some history of vectors:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Abstract_linear_spaces.html

other interesting articles about history of math and physics in the same site:

http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html


Dante.

 

[Integral]

The universal law of gravitation was developed by Newton when he was in his early 20's (around 1665) and published in his Principia Mathematica in 1887.

I am sure you mistyped, that should be 1687!

 

[Meir Achuz]

My understanding is that Newton delayed publication of his Principia because he took a while to prove that large spherical objects (like the Sun and Earth) behave like point particles in gravity. He didn't have Gauss's law so had to use an ingenious, but complicated, geometric proof. I recall seeing an English translation of Newton's Principia at Barnes and Noble.