[Vo]:Groking CoAM, Kepler and Rossi
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
Re: [Vo]:Groking CoAM, Kepler and Rossi
Bravo Steven, it sounds like you have been having a good time in your path of discovery. I find myself in the same boat on occasions where I discover something that is new to me but then I find that it has been documented by others and recently wikipedia has been my worst foe. At least you and I have the satisfaction of knowing that we are venturing into the unknown. I like to think of my new concepts as suggesting that I could have been there first, but was not. Regardless of the timing, it is mind opening to venture into these types of studies. Much is learned about the natural world by actually exploring interesting concepts. When the pieces fall together we get a better view of the entire picture that tends to remain in our memories far longer than one can recall a equation. And as you suggest, unusual modifications from the original well known paths lead to interesting observations that might not make sense at the first look. I have a tendency to think differently than others about natural phenomenon. You appear to exhibit that curse as well! This type of reasoning has served me well in the past when I have solved extremely complicated problems that have been unresolved for months until an unorthodox idea appears. The more we think about things in a different manner, the more likely it is to stumble upon these wondrous ideas. Keep stressing your mind as it is extremely good for you. A number of years ago I played chess with some very good players and I suspect that you may have done the same. That should be a requirement for guys and gals that want to enter into the engineering or science fields in the future. The deep planning necessary to play chess at a reasonable level is greatly advantageous for problem solving. I find the CoE as a very useful guide as well. That along with the CoM, coupled with a observation reference change can make many problems become much more transparent. I wish you good fortune my friend. Dave -Original Message- From: OrionWorks - Steven Vincent Johnson orionwo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Sun, Jun 24, 2012 6:25 pm Subject: [Vo]:Groking CoAM, Kepler and Rossi INTRODUCTION: What do you do when you are trying to grasp the fundamentals of a well-known hysics equation, an equation you had not been formally taught it in school? ikipedia, of course! But what happens if what Wikipedia has to say on the ubject confuses you even more? You do your best to reason out the undamental elements that comprise the equation on your own recognizance. ou hope that what you come up with will somehow miraculously match up with hat the academic textbooks have to say on the subject. The process of discovery can occasionally lead to surprising conclusions, specially when you get around to comparing notes with what the priesthood f physics has to say on the subject. You might discover the fact that while our version of the equation seems to posses fundamental differences when ompared to what is formally laid out in the textbooks, what you came up ith nevertheless seems to explain the phenomenon in exactly the same way. ot only that you can use your own equation to make the exact same redictions. This recently happened to me while trying to grok a well know algebraic ormula, the Conservation of Angular Momentum, or CoAM. It is intimately elated to my on-going study of Celestial Mechanics through the use of omputer simulation. Here's one of my prior posts pertaining to personal esearch 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 he fundamentals of CoAM because I came to realize that the equation is an ssential part of the physics that helps explain how Celestial Mechanics CM) behaves. CoAM helps explain why a satellite orbiting a gravitational ass, like a planetary body, typically assumes the path of an ellipse where ne of the foci is located at the center of the planetary body. Why does the elocity of an orbiting satellite as it swoops away from the planetary mass low down? CoAM explains it. Why does the satellite's velocity speed up ramatically during the return phase. Again CoAM explains the reason why. hat is even more astonishing is why does the speeding satellite after it as made its nearest approach break away? How can that possibly happen? Why oesn't it crash into the planetary body since the gravitational influence eing felt would be at its greatest strength? Again, CoAM explains why that oesn't happen. I would conjecture that exactly how CoAM constantly comes to he rescue is not necessarily that well groked by most folks, including hysicists. I certainly didn't understand nor appreciate the incredible ance of physics that is involved, not until I started taking a long hard ook. It is my hope that how I finally learned to grok CoAM might help others who ay also
