June 26, 2018 Tuesday
Bedtime Story
How Lagrange Related Himself to Newton
Last night we got a fair understanding of
how analytical mechanics (both Lagrangian and Hamiltonian) differs from Newtonian
mechanics.
No new views of classical physics need to
be applied while applying these two other forms of mechanical analyses which
means to say that the essential concepts of physics remains unchanged.
The best way to describe analytical mathematics
of Lagrange and Hamilton is that they are a set of equivalent formalisms that
have broad applications to classical mechanics.
The beauty is that this technique goes even
further and the same principles are applicable to relativistic mechanics and
general relativity.
With some alterations, these are even
applicable to quantum mechanics and quantum field theory.
That is the power of mathematics for you.
Many of you may feel that Lagrangian
mechanics is merely a reformulation of Newtonian mechanics, which is not
completely wrong but it goes further.
Lagrangian mechanics plays a vital role in
providing a deeper understanding of physics.
It seems from one of the quotations of
Lagrange that intellectually he considered himself at par to Newton.
So much so that he believed in his mind
that he would have himself discovered what Newton did had Newton been not the
first one to beat him to it.
This is not very overtly stated but the
above implication is hard to miss for anyone who is skilled at reading between
the lines.
“Newton was the greatest genius that ever
existed, and the most fortunate, for we cannot find more than once a system of
the world to establish.”
Of course, Lagrange never lived to see the
revolution of relativistic physics that would start some eight decades or so
after his death.
He was right is saying that Newton was the
greatest genius that ever existed, though we was surely wrong in his second
half of the comment, as there indeed was someone who did found out more than
once a system of the world that still boggles our minds.
Lagrange though was very confident of the
revolutionary nature of his work in Mécanique analytique and this is what he
had to say about it:
“We have already various treatises on
Mechanics, but the plan of this one is entirely new.
I intend to reduce the theory of this
Science, and the art of solving problems relating to it, to general formulae, the
simple development of which provides all the equations necessary for the
solution of each problem.
I hope that the manner in which I have
tried to attain this object will leave nothing to be desired.
No diagrams will be found in this work.”
We shall continue with Lagrange’s
assessment of his own work of analytical mechanics in the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
Advertisements
Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
No comments:
Post a Comment