Julian, I agree with a lot of what you say about the importance of not ignoring innovative solutions. And agree that way too little has been done with operation at resonance. But is that necessary anymore? With today's computers and free programs anyone can solve resonance problems overnight.
This is innovative intellectual freedom of the best kind!!
A BIT ABOUT MATH:
Resonant mathematics exist and are quite well understood. The mathematics of resonance used to require a lot of study, although the path to that understanding was well known even a hundred years ago. Now a home computer running inexpensive programs that will solve resonant problems in dynamic systems quickly and simply. Today anyone with a good or better high school education can set up and let the computer solve resonant problems overnight......the same problems that just 20/30 years ago required a year of Ph.D. time.
Yes, you are correct that there is no symbol for resonance in traditional calculations. There couldn't really be a symbol for it because mathematical resonance isn't something that exists by itself. It is simply a special condition that exists throughout a set of answers when a differential equation describing a dynamic system is solved for frequency. There is no single solution. What happens mathematically is that sometimes a portion of a dynamic solution set "blows up" in one energy realm or another and that is what is popularly come to be called "resonance".
A SITE WORTH LOOKING AT (but not too long...):
I'm no teacher, just a retired engineer who needed to consider resonance now and again. For folks that enjoy math, go to this site for a great introduction to old style resonance calculations. Believe it or not, engineers actually used to do this sort of thing with a pencil and paper. Some of us are so old that we remember when hand calculators came out! What an advance that was!
"(warning, there is some deep stuff there). If you want to do it an easier way just read on........
NOW ANYONE CAN INNOVATE AND INVENT THE EASY WAY!
That website was weird, beautiful, and yuk all at the same time. But the important thing is how our society has progressed. Spending years to do that kind of thinking is now optional.
It's no longer necessary to waste innovative energy.
Nifty and fun tho' those hand calculations can be, it is simply is not necessary to do things longhand anymore and also equally unnecessary to spend years learning math and physics. Now anyone and everyone can innovate. All it takes is a home computer, download a dynamic modeling program , spend an evening figuring how to work it, model something, and get to dreaming. The program will handle calculations and advise of errors. Innovation is what people do best anyway.
Roger L.
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----- Original Message -----From: Julian WebbSent: Thursday, May 23, 2013 3:11 AMSubject: Re: [Electric Boats] "Batteries Not Included"SNIP...- To cut a long story short unless the importance of electrical and mechanical resonance in systems is appreciated, (which has no place, constant or symbol in any traditional calculations or formulas that I have ever seen) they cannot be understood or replicated.
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