Ralph White

0 Reputation

3 Badges

17 years, 357 days

MaplePrimes Activity


These are replies submitted by Ralph White

I found the problem. I was using the call Bodeplot. I need to use BodePlot. I made an error in typing the command and capitalization. It works now. Sorry for my error. David P.
I found the problem. I was using the call Bodeplot. I need to use BodePlot. I made an error in typing the command and capitalization. It works now. Sorry for my error. David P.
The examples on the help page do not work(no graphs). If I paste the examples into a document, no graph is plotted. It appears to not recognize that the package is loaded... Here is an example: > with(DynamicSystems); [AlgEquation, BodePlot, CharacteristicPolynomial, Chirp, Coefficients, ControllabilityMatrix, Controllable, DiffEquation, DiscretePlot, FrequencyResponse, GainMargin, Grammians, ImpulseResponse, ImpulseResponsePlot, IsSystem, MagnitudePlot, NewSystem, ObservabilityMatrix, Observable, PhaseMargin, PhasePlot, PrintSystem, Ramp, ResponsePlot, RootContourPlot, RootLocusPlot, RouthTable, SSModelReduction, SSTransformation, Simulate, Sinc, Sine, Square, StateSpace, Step, System, SystemOptions, ToDiscrete, TransferFunction, Triangle, Verify, ZeroPoleGain, ZeroPolePlot] > sys1 := TransferFunction(2200*s/((s+1100.000000+9939.315872*I)*(s+1100.-9939.315872*I))); module () export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; end module > sys2 := TransferFunction(22000*s/((s+15582.57569)*(s+6417.424305))); module () export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; end module > Bodeplot(sys1); Bodeplot(sys1) > Any help is appreciated. Thanks.
The examples on the help page do not work(no graphs). If I paste the examples into a document, no graph is plotted. It appears to not recognize that the package is loaded... Here is an example: > with(DynamicSystems); [AlgEquation, BodePlot, CharacteristicPolynomial, Chirp, Coefficients, ControllabilityMatrix, Controllable, DiffEquation, DiscretePlot, FrequencyResponse, GainMargin, Grammians, ImpulseResponse, ImpulseResponsePlot, IsSystem, MagnitudePlot, NewSystem, ObservabilityMatrix, Observable, PhaseMargin, PhasePlot, PrintSystem, Ramp, ResponsePlot, RootContourPlot, RootLocusPlot, RouthTable, SSModelReduction, SSTransformation, Simulate, Sinc, Sine, Square, StateSpace, Step, System, SystemOptions, ToDiscrete, TransferFunction, Triangle, Verify, ZeroPoleGain, ZeroPolePlot] > sys1 := TransferFunction(2200*s/((s+1100.000000+9939.315872*I)*(s+1100.-9939.315872*I))); module () export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; end module > sys2 := TransferFunction(22000*s/((s+15582.57569)*(s+6417.424305))); module () export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; end module > Bodeplot(sys1); Bodeplot(sys1) > Any help is appreciated. Thanks.

Here is a summary of the solution described by Panayotounakos in his article:

http://patrick.toche.free.fr/research/papers/abel.pdf

I have not yet written a maple worksheet to check the numerical validity of the reported solution.

then evaluate the resulting integral numerically from zero, or simplyfying simbolically, no polylog on sight ...and a rather simple and simmetrical solution

involving only arctanh and arccos. here the indefinite integral


  1|/2          1   (.25*arccos(x)^2+1)*|/2)
----- arctanh ---- -------------------------- +
   4            2  |/(.25arccos(x)^2 +1)


            1     (.25*arccos(x)^2-1)*|/2)
- arctanh(---- -------------------------
            2      |/(.25arccos(x)^2 +1)

 

F.

hope have been right ... ciao

In spite of the megabugaerror,

I am still alive

^_^

be good

f

HI

is my first time in high mathematics quarters of maples...

Has been a bit frustrating trying solving the Integral the old way, by paper and triks, substitutions and so... even more frustrating when I gave a try with matematica: not a second and here the solution (do know if is the right one, but it seams old fashon enough to be so): 

(1) input: [Integral]ArcTan (x)/(1+x^4) dx
 
(2)output: 1/2 ArcTan (ArcTan[x2])
 
(3)output: diff (integral output)->((ArcTan x)/(1+x4)) just to verify I were awake...
 
(4) imput: evaluate Int, x=1..4
 
(5) Output: 1/4 ArcTan ((-Sqr(2)*p+8 ArcTan[16]+Sqr(2)*(ArcTan[(4 *Sqr(2)/15]+ArcTanh[(4*Sqr(2)/17]))
 
What do you thinck, it is just allucination or ...
in any case how to know if a math prog gibes the right answers, in such unhandly cases?!
 
Thanks for the great insight which comes out from your discussion, I'm notv a mathematician though i have great passion for it ... as it happens quite often about the prittiest girl in the school...
 
Behave, if not
 
be good!
 
Federiclet(ITA)

 

hello

here a list of few books which might peraphs tur to be usefull to you:

George GAMOW, Gravity, Doubleday Anchor, Science & Study Series, (N. 8, 22)

George GAMOW, Mr. Thomkins in Paperback, Cambridge Univ Press (1993)

Peter G. BERGMANN, The riddle of gravitation, Dover (New York, 1992)

Einstein, Lorentz, Weyl, Minkowski,The principle of relativity, A collection of original papers on the special and general Theory of Relativity, notes by Sommerfeld, Dover (New York) re-edition of 1952 Collected papers.

Einstein's miraculous year. Five papers that change the face of physics, Princeton Univ Press, 1998

Hans REICHENBACH, The philosophy of space & time, introductory remarks by Rudoilf CARNAP, Dover (New York) new english translation of the first edition 1957 in English, of H. R. Philosophie der Raum-Zeit-Lehre(original dating 1953).

It is a great book whith a rich bibliography up to date and of historical and prosographycal meaning.

 

Ciao

Take care

Federiclet

 

 

Is it the Gravitation circle here? I guess, so no better  place where to get attracted non earth  strings  attached, ops I almost dismissed the other … holy strings the supadupa strings of the unifying Theory  Quest ….
No joking to much, I hope.
The subject:

1) the Newtonian gravitation law supposes a intertial absolute frame, plus Cavendish experiment s and so on gave an experimental verification of F= k*(M*m)/(R^2) not too faar from human touch and normal sight …. 2) This is the ontic side of the issue, lets go at the ontological side:a) why interacting mass do not add up, but multiply their action? b) isn’t it possible hat the Newtonian law contains already enough  information aiming to quanto-gravitational theories?


The questions are linked, in my mind, of course, by a series of neural strings connecting: the product of masses to a statistical sight (probability of independent but related events – the coins & Binomial – multiply, 2a) by equating M to m --> m^2 woul be a perfect square of a probable mass operator”, c) where to disguised the hidden wave function? The best place were to look is a the Gravitational field, calculating the potential U= - k* (Mm/R).


The results requiring heavy critics and suggestions:

1) since equating the masses, in the sense of considering a single mass and its "virtual" double, is improper in Newtonian theory frame, could be that labeling somehow the equated mass by “I” the imaginary unity would have help. So I had done it.


U= - (k im*m)/R  -> (U/m) = -(k i m)/R. -> (U/m) + (k i m)/R =?.

Here is the critical point, peraphs since I deliberatly I tought that what =0 for real values, could = z in the complex frame i’m trying to get out  of / or fit in (?) the classic formula. I then equated  the upper right side to a possibly mock complex variable Z,  followed by rising the formula as a pover of “e”-> e^Z=e^(U/m) * e^(k I m)/R,
Recalling that Z=a+iB is equivalent to e^Z=e^a *(cos(b) +I sin(b)) (cfr Wunsh, Complex Variables p 96.97)
I proceeded conformably  

e^Z=e^(U/m) * (cos((km)/R) + I  sin ((km)/R)


The equation identify clearly a real and an imaginary component of the potential energy, and what most intrigues is the wave form of both:

                       Re                                           Img
e^Z = e^(U/m) * (cos((km)/R) + I e^(U/m)* sin ((km)/R)


Reonsidering the initial condition Z=0 the equation becomes
 

(e^-(U/m))= (cos((km)/R) + I e^(U/m)* sin ((km)/R)


Practically we are facing two orthogonal waves, the cos Real valued wave, and rotate of 90° by I multiplication sin wave, with a difference in period  of Pi/2.
The waves are mainly concentrated within the unit disk. It's there the maximal density and wide change in period spectra, because of R at denominator at the cos and sin arguments.


Though very clumsy, and bound to a thin hope about the legitimacy of introducing I when equating masses, guess the scenario offered at the end, is rather fascinating. Somehow it relates to the inner behavior of the mass its-self, and possibly with its peculiar way of originating as “a double vitual-real”. In my view m^2 instead of M*m, is the Unitarian subject of the gravitational law. though it must be intended analogically because of the dynamic double). The orthogonal waves, (vector  basis of a possible mass field?), oscillating asynchronously must show further consequences in terms of gravitational energy /mass distribution and mass motion and interaction: as a “particle” &/or as a “2 waves packets”.


Hope finding many critics to all this, and some help  to get things done properly.
Thanks for your attention.
Federiclet
 

 

 Ciao,

I just like recall an 'arithmatical expression' discussed by Euler in onenof his books (I'll be more precise a second time, possibily). The expression is (x^x). I hope BillFish will not be hurt id i link x^x to is b^x, tinking of the first as a genralization of the second.

Euler spotted many peculiar propreties of x^x.

1) also if is somehow "plottable" as y=x^x, the curves is almoust everywere indetermined in its codomain, (y).

Except for Natural Numbers, already the Rationals gives undecidable results, in particular if they ar unlimited fractions. In this case, the question about the nature of the output of x^x, will requires  singular case study for each x, or finding a general theorem in Numer Theory that states once for all to which class this ouput X^X belongs.

Whit Irrationals, the case is even more obvoius, since if had already by a great deal of work demonstrating the irrationality of 21/2, 51/2, 71/2, 21/3, 111/4 and of the sum 21/2+31/2 .... and not much further than this (cfr. Hardy & Wright, Oxford 1978), it is very plausible how problematic will be determining the nature of (x irr) ^ (x irr). Which means that for the Irrationals the curve is maynly indetermined.

Finally taking into account the Trascendental numbers the question gets even deeper for the reason that, though they have the same Cardinal of the continuum, we know really a little about them. The numbers  "e", "Pi", "ln2", "ln3/ln2", "e Pi ", "2^(1/2) ", J0(1) had been shown tey areTrascendental, but not jet  "2^ e ", "2^ Pi ", "Pi^ e ", or the Euler's constant "gamma".  For the Trascendental we can say the the curve is twice indetermined, knowing just a few of the numbers and so of the x on which something can be said as comes uot to determine the nature of y=x^x.

Euler goes into alla possible combinations amongst the clases of numbers. To show as x^x si such a peculiar mathematical object.

I think for any of you which master Maple tis "object" could be an interesting to get a plot (not by approximation), and I bet the proper realm of parametrization will be the complex one. The reason I say this comes from the mapping propreties of x^x, especially if one takes the combinatorics of N, Q, Z, T, lets say x natural over x rational the simplest expression that already entrains irrational as x^x,  or even trascendental, for certain numerical combination that possibily could'nt fit in the original imput  classes.

The Curve y=x^x over R, could be also intriguing for the fact tha it seams nowere dense, (always not taking into consideration the approximation wich allow us to see it as a continuos line, iperexponential also). Esplicitly the mesure of the line, over a limited sets of values, must be fractal.

Taht's it.

This I think can explain, peraphs, the behawiour of "a+b^x" that surprize BillFish, and the aidea that this alla might have to do with God. On a different step, Goedel profess atheist, gave a go him too to the Onthological Pouf of Gog, using modal Logic, and a similar approach he used to answer definitively at Rieman hypotesis on artmetization of Mathematics (as you know the answer was "no"). Cantor too, by setting is Meditation on Transfinite Numbers, felt his work very closed to a quest for God.

So BillFish, you are in a very good company!!!

Take care

Federiclet

 

 

 

 

fEdErIcLeT

Thank you Dave. Your suggestion worked.
Thank you Dave. Your suggestion worked.
Thank you. I will try it and see if I understand it. I appreciate your efforts in helping me to understand this tool.
Thank you. I will try it and see if I understand it. I appreciate your efforts in helping me to understand this tool.
1 2 Page 1 of 2