INTRODUCTION:
What do you do when you are trying to grasp the fundamentals of a well-known
physics equation, an equation you had not been formally taught it in school?
Wikipedia, of course! But what happens if what Wikipedia has to say on the
subject confuses you even more? You do your best to reason out the
fundamental elements that comprise the equation on your own recognizance.
You hope that what you come up with will somehow miraculously match up with
what the academic textbooks have to say on the subject.
The process of discovery can occasionally lead to surprising conclusions,
especially when you get around to comparing notes with what the priesthood
of physics has to say on the subject. You might discover the fact that while
your version of the equation seems to posses fundamental differences when
compared to what is formally laid out in the textbooks, what you came up
with nevertheless seems to explain the phenomenon in exactly the same way.
Not only that you can use your own equation to make the exact same
predictions.
This recently happened to me while trying to grok a well know algebraic
formula, the Conservation of Angular Momentum, or CoAM. It is intimately
related to my on-going study of Celestial Mechanics through the use of
computer simulation. Here's one of my prior posts pertaining to personal
research I've done in the field made back in March of 2012:
http://www.mail-archive.com/vortex-l@eskimo.com/msg64010.html
While continuing my research I eventually realized I needed to understand
the fundamentals of CoAM because I came to realize that the equation is an
essential part of the physics that helps explain how Celestial Mechanics
(CM) behaves. CoAM helps explain why a satellite orbiting a gravitational
mass, like a planetary body, typically assumes the path of an ellipse where
one of the foci is located at the center of the planetary body. Why does the
velocity of an orbiting satellite as it swoops away from the planetary mass
slow down? CoAM explains it. Why does the satellite's velocity speed up
dramatically during the return phase. Again CoAM explains the reason why.
What is even more astonishing is why does the speeding satellite after it
has made its nearest approach break away? How can that possibly happen? Why
doesn't it crash into the planetary body since the gravitational influence
being felt would be at its greatest strength? Again, CoAM explains why that
doesn't happen. I would conjecture that exactly how CoAM constantly comes to
the rescue is not necessarily that well groked by most folks, including
physicists. I certainly didn't understand nor appreciate the incredible
dance of physics that is involved, not until I started taking a long hard
look.
It is my hope that how I finally learned to grok CoAM might help others who
may also occasionally feel disenfranchised from what traditional physics
books might have to say on similar subjects. The experience lead me to a
belief that there may turn out to be many roads that lead to the Grand City
of Rome. Not only that, sometimes traveling down a less beaten path can have
its own unique surprises and rewards. I suspect Andrea Rossi is a perfect
example of such an individual who found his own unique pathway to the City
of Rome. I suspect he chose a road rarely travelled by others. The path he
chose could possibly end up turning the world of physics upside down -
assuming his eCats really do work, and perhaps most important of all, he
gets the chance to sell them en masse to the world.
MY SEARCH FOR COAM BEGINS:
Initially I tried reading what Wikipedia had to say on the subject. The
authors weren't of much help to me. See:
http://en.wikipedia.org/wiki/Conservation_of_angular_momentum#Conservation_o
f_angular_momentum
http://tinyurl.com/yf28c7l
Something was missing. Nowhere in the all of the turgid mathematical
equations that had been written down was there the slightest hint of a
squared value. That bothered me. It bothered me because of my own extensive
computer simulation research into Celestial Mechanics, of how orbital bodies
are attracted to a central gravitational mass. I was also acutely aware of
Kepler's most famous law concerning planetary motion, his 2nd law which
states:
A line joining a planet and the Sun sweeps out equal areas during equal
intervals of time
Kepler's 2nd law introduces a constant that manifests in our
three-dimensional universe in the form of a flat and fixed 2-dimensional
piece of area. No matter what shape that flat patch of area assumes the
amount of area remains constant. First a qwik refresher course on "area". An
area, such as a rectangle, is determined by multiplying two 1 dimensional
lengths held at 90 degrees to each other. It is often expressed as:
area = x * y.
If, as sometimes happens, x = y, representing a square, then you can
simplify the rectangular equation to:
area = x^2.
There was the squared value! Based on my own experience of working with
computer simulations of orb