June 23, 2018 Saturday
Bedtime Story
Constraints of a Physical System
One of the well known scalar quantities is
the temperature since it just needs a single set of integers (along with the
appropriate units) to quantify it.
Other such examples of scalars are well
known to you and they include mass, charge, volume, time, speed and charge
density.
Here a word of caution has to be made; the
quantities that are scalars in classical mechanics have to undergo
modifications in relativistic physics.
These classical scalar quantities will need
to be combined with other quantities and then treated as 4-vectors or tensors
in relativistic physics.
An example of this would be charge density
at a point in a medium which is a total scalar in classical mechanics.
Yet in relativistic physics it needs to be
combined with local current density which is a 3-vector to give a relativistic
4-vector.
Let us not go too much into relativistic
physics as that will certainly confuse you (and me as well).
The point that I was making earlier was
that in contrast to Newton, Lagrange developed mathematics in classical
mechanics that would make use of scalar quantities to arrive at the same
elegant solutions that Newton achieved.
The mathematics that was developed by
Lagrange, Hamilton and others goes broadly by the name of analytical mechanics
or sometimes more specifically as Lagrangian mechanics as homage to the
founding father of this field of classical mathematical physics.
While Newtonian mechanics attacks the
problem of moving objects directly, Lagrangian mechanics does it more subtly
making use of the constraints that are inherent in the physical systems.
What do we mean by constraints and how are
they inherent in a physical system?
These are critical questions that every
child should be made to understand in order to emphasize that nature operates
on certain principles that cannot be defied and perhaps this can help take out
magical thinking that most of come endowed with and then gets culturally
reinforced and later permanently embedded mentally.
A constraint of any physical system in
classical mechanics is any parameter that a system must obey.
Just to give one very banal example that
you have often dreadfully encountered in your high school exams of a block of
wood sliding down a slope marked across with several arrows pointing down, up
and at right angle to the slope along with trigonometric functions attached to
them with angle dependent on the angle of the slope.
In such a system what is the constraint?
The constraint is, particularly when it
comes to deriving your solutions, is that the block of wood has to be in
contact with the slope all the time.
The alternatives of the block flying around
it or tunneling through it are not permissible.
Now this is a very loose definition of a
constraint but you get the idea what is implied by a physical system having a
complaint.
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.
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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:
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