May 29, 2018 Tuesday
Bedtime Story
Solutions to n-body Problem Needs Explanation
Last night I had left you with a promise to
list out the solutions to the n-body problem (whose specific case is the
two-body problem) but I realize that it is not that a facile task.
Ground work has to be laid before the
solutions can be proposed.
Some terms that are listed out below are
familiar to most such as mass, position, vector but there are some other terms
that needs more detailed consideration.
The masses of the two bodies are
represented by m1 and m2.
Position of one body relative to the other
is given by the vector r.
The distance between the two is represented
by r, all in the standard SI units of course.
One of the key concepts in the two body
problem that needs to be introduced is the specific relative angular momentum
represented by small letter h with an arrow on top but I will simply use the
small letter h here.
This is a mass-specific angular momentum
and angular momentum as you would recall is the rotational equivalent of linear
momentum and is conserved quantity.
When we say it is a conserved quantity it
means that the total mass-specific angular momentum of the two bodies does not
change unless acted upon by an external torque.
Torque is similar to force but is used when
we apply the idea of force to change of angular momentum.
Now whenever you come across the words
conservation and law together, treat them with great reverence, only in physics
of course; everywhere else these terms would most likely be not only misused
but thoroughly abused as well.
There are far more charlatans and spiritualists
chanting out there nonsensical mumbo jumbos sexed up with borrowed lexicon of
physics and mathematics (more from physics usually as it is the most
fundamental of natural sciences) than there are genuine physicists and
mathematicians on our dear 4.6 billion years old planet.
Conservation laws of physics are
fundamental is describing the real world or the nature as Feynman use to call
it; even though mathematics is the queen of sciences and widely used in physics
mathematical equations do not always describe reality and yet they may be
either true or logically derivable.
It is the physics that is by far, the best
in describing reality though it still does not answer the question ‘Why’ but
rather ‘How’.
One can safely say that all of the physics
rests on these conservation laws and it is these laws that determine what
processes are permissible in nature and what are not.
Once when I say that conservation laws are
fundamental to physics, it necessary implies that they have broader and wider
implications to other sciences such as chemistry, biology, geology, astronomy
and it is endless.
Science cannot have it that some laws are
applicable at one place and defied at other; this is the fundamental philosophy
of unity of science because the different subjects of science are merely
examining the same nature at different levels of organization.
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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