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Hi everybody;

In the following attached file, I am trying to solve a system of nonlinear equations with one equality constraint. I have 9 equations and 9 unknowns. Attached file has composed of 3 main parts, first is input data, second is the 9 nonlinear equations from E_1 to E_9 and finally third part is constraint equation called C_1. My unknowns are "phi, theta, p, q, r, T, L, M and N". My question is that: Can Maple solve this problem?? Is there any solution to this problem or I have to change input data?? If Maple can solve this problem, how can I do that?? 

I appreciate your help in advance.

NL.mw

The mechanism of transport of the material of the sewing machine M 1022 class: mathematical animation.   BELORUS.mw 




  Continuation.
  One way to get rolling without slipping animation in 3d. The trajectory and circle are divided into segments of equal length. In the next segment of the trajectory we construct circle, taking into account the fact that it turned on one segment. Rolling sphere or cylinder can be simulated, if we take plottools templates of the same radius, and replace them on the site of our circle.

ROLLING_WITHOUT_3d.mw













Howdy all,

I am trying to fit an exponential and logistical model to a set of population data i've been given using the NonlinearFit function in the statistics toolbox. When try to find the fit for the exponential function I get an error saying "SVD of estimated Jacobian could not be computed". Furthermore, when I display the regression over the set of data points all it shows is a horizontal line. I'm not sure how to go about fixing this. My data set is only 17 points and my input function is about as simple as it gets.

When I run the program to solve for logisitcal model I do not get the error but the displayed plot still shows just a horizontal line dispite the function being non-linear.

So far I have...

regE := NonlinearFit(a*exp(b*x),year,population,x)

regLog := NonlinearFit(a/(1+b*exp(-c*x)),year,population,x)

expon := plot((regE), x = 1850..2020):

logi := plot((regLog), x = 1850..2020):

display({data,logi,expon});

I have not tried using optimization yet but I will soon although I'm not sure if it will improve my results since my undertanding is that they both use the same process to estimate the parameters.

Anyways, Thanks for the help in advance!!

 

EDIT: Here is the data I am using.

year := [1850,1860,1870,1880,1890,1900,1910,1920,1930,1940,1950,1960,1970,1980,1990,2000,2010]:

population :=[4668,9070,17375,27985,37249,63786,115693,186667,359328,528961,806701,1243158,1741912,2049527,2818199,3400578,4092459]:

 

 

The method of solving underdetermined systems of equations, and universal method for calculating link mechanisms. It is based on the Draghilev’s method for solving systems of nonlinear equations. 
When calculating link mechanisms we can use geometrical relationships to produce their mathematical models without specifying the “input link”. The new method allows us to specify the “input link”, any link of mechanism.

Example.
Three-bar mechanism.  The system of equations linkages in this mechanism is as follows:

f1 := x1^2+(x2+1)^2+(x3-.5)^2-R^2;
f2 := x1-.5*x2+.5*x3;
f3 := (x1-x4)^2+(x2-x5)^2+(x3-x6)^2-19;
f4 := sin(x4)-x5;
f5 := sin(2*x4)-x6;

Coordinates green point x'i', i = 1..3, the coordinates of red point x'i', i = 4..6.
Set of x0'i', i = 1..6 searched arbitrarily, is the solution of the system of equations and is the initial point for the solution of the ODE system. The solution of ODE system is the solution of system of equations linkages for concrete assembly linkage.
Two texts of the program for one mechanism. In one case, the “input link” is the red-green, other case the “input link” is the green-blue.
After the calculation trajectories of points, we can always find the values of other variables for example the angles.
Animation displays the kinematics of the mechanism.
MECAN_3_GR_P_bar.mw 
MECAN_3_Red_P_bar.mw

(if to use another color instead of color = "Niagara Dark Orchid", the version of Maple <17)

Method_Mechan_PDF.pdf






Hello,

I would like to plot gait diagrams (the lines you can see on the picture belowà from the solutions obtained with a NL oscillator (composed with 8 coupled odes). Here the result that I would like to obtain.

Initial plot:

 

Desired plot

 

 

I would like to obtain 4 lines corresponding to the 4 elliptic trajectories obtained with the NL oscillator. The four lines should be done like this. When the trajectory is above 0, the line should be colored in green. When the trajectory is below 0, the line should be colored in black. 

May you help me to define this kind of graph called gait diagrams from the solution of the NL oscillator ?

Here you can find my maple code:

K:=Matrix([<0, -1, 1, -1>,<-1, 0, -1, 1>,<-1, 1, 0,-1>,<1, -1, -1,0>]);

for i to 4
do
r[i]:=sqrt((u[i](t))^2+(v[i](t))^2):
omega[i]:=omega[sw]/(1+exp(b*v[i](t)))+omega[st]/(1+exp(-b*v[i](t))):
Equ[i]:=diff(u[i](t),t)=Au*(1-r[i]^2)*u[i](t)-omega[i]*v[i](t):
Eqv[i]:=diff(v[i](t),t)=Av*(1-r[i]^2)*v[i](t)+omega[i]*u[i](t)+MatrixVectorMultiply(K,<seq(v[i](t),i=1..4)>)[i]:
EqSys[i]:=[Equ[i],Eqv[i]]:
end do:

paramsCycle:=omega[st]=4*2*Pi,omega[sw]=2*Pi,Au=5,Av=50,b=100;
params:=paramsCycle;

Differential system 
sys:=map(op,eval([seq(EqSys[i],i=1..4)],[params]));
ic:=[u[1](0)=0, v[1](0)=0,u[2](0)=0, v[2](0)=-0.1,u[3](0)=0, v[3](0)=0.1,u[4](0)=0, v[4](0)=0.1];
Résolution1
res:=dsolve([sys[],ic[]],numeric):
Initial boundaries
tcalc:=4;
ic2:=[seq(u[i](0)=eval(u[i](t), res(tcalc)),i=1..4),seq(v[i](0)=eval(v[i](t), res(tcalc)),i=1..4)];
Résolution2
res:=dsolve([sys[],ic2[]],numeric):

tmax:= 40:
numpts:=100*tmax:
plots:-odeplot(res,[t,v[1](t)],0..tmax,thickness=2, view=[0..5, -1.5..1.5],numpoints = numpts);
plots:-odeplot(res,[t,v[2](t)],0..tmax,thickness=2, view=[0..5, -1.5..1.5],numpoints = numpts);
plots:-odeplot(res,[t,v[3](t)],0..tmax,thickness=2, view=[0..5, -1.5..1.5],numpoints = numpts);
plots:-odeplot(res,[t,v[4](t)],0..tmax,thickness=2, view=[0..5, -1.5..1.5],numpoints = numpts);
plots:-odeplot(res,[seq([t,v[i](t)+i*5],i=1..4)],0..tmax,thickness=2,view=[0..5,0..25], numpoints = numpts);

Thanks a lot for your help

I want to obtain polynomial representation of my data:

with(Statistics):

X:=Vector([huge data package-X],datatype=float):

Y:=Vector([huge data package-Y],datatype=float):

NonlinearFit(c*t^2+b*t+a, X, Y, t)

but I can't see any result. What's the problem?

My worksheet: He_p=f(t).mw

I am trying to solve 4 nonlinear equations for four variables using fsolve  and the output that i am getting is basically the same equations repeated after some time.  I even tried reducing one of the equations using assumptions from my side but it results in same behaviour..  Quite new to maple, would like some advice as to this behaviour. Thanks

 Here's the file

fsolve_1.mw

 

PS- using do loop is part of the solving so i cannot remove that

Hi all,

I need to solve det[M]=0 for omega.

M is:

M := Matrix(8, 8, {(1, 1) = BesselJ(n, tp*a), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = -BesselJ(n, tg*a), (1, 6) = -BesselY(n, tg*a), (1, 7) = 0, (1, 8) = 0, (2, 1) = k*n*BesselJ(n, tp*a)/(tp^2*a), (2, 2) = I*k*n*mu0*omega*(diff(BesselJ(n, tp*a), a))/(tp^2*a), (2, 3) = 0, (2, 4) = 0, (2, 5) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (2, 6) = -k*n*BesselY(n, tg*a)/(tg^2*a), (2, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (2, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (3, 1) = 0, (3, 2) = BesselJ(n, tp*a), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = -BesselJ(n, tg*a), (3, 8) = -BesselY(n, tg*a), (4, 1) = -I*omega*`&varepsilon;p`*(diff(BesselJ(n, tp*a), a))/tp^2, (4, 2) = k*n*BesselJ(n, tp*a)/(tp^2*a), (4, 3) = 0, (4, 4) = 0, (4, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (4, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (4, 7) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (4, 8) = -k*n*BesselY(n, tg*a)/(tg^2*a), (5, 1) = 0, (5, 2) = 0, (5, 3) = k*n*BesselY(n, t0*b)/(t0^2*b), (5, 4) = I*mu0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (5, 5) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (5, 6) = -k*n*BesselY(n, tg*b)/(tg^2*b), (5, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (5, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (6, 1) = 0, (6, 2) = 0, (6, 3) = BesselY(n, t0*b), (6, 4) = 0, (6, 5) = -BesselJ(n, tg*b), (6, 6) = -BesselY(n, tg*b), (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = BesselY(n, t0*b), (7, 5) = 0, (7, 6) = 0, (7, 7) = -BesselJ(n, tg*b), (7, 8) = -BesselY(n, tg*b), (8, 1) = 0, (8, 2) = 0, (8, 3) = -I*epsilon0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (8, 4) = -k*n*BesselY(n, t0*b)/(t0^2*b), (8, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (8, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (8, 7) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (8, 8) = -k*n*BesselY(n, tg*b)/(tg^2*b)});

and n=0,1,2.

Except of omega and k ,other parameters is canstant.

After using
with(LinearAlgebra):
detM := Determinant(M):

I used solve(detM=0,omega) and fsolve() but it dosnt work. how can i solve it?

Thanks alot.

hi .please see attached file below and help me

thanks..indices(res_nolist).mw

hi.may  help me for solve this nonlinear equations by numeric solver maple39.d39.pdfocx39.pdf

thanks alot

file format is pdf and word type

 

LE.2a.E.LGM.mwHi, my this programme is executing for linear part but does'nt show the proper results for non linear,plz tell me appropriate code

hi .how i can solve nonlinear equation with unknown prameter omega as below

thanksfrekans.mw

I want to solve numerically the nonlinear pde:

 

u_x+u_t - (u_{xt})^2 = u(x,t)

 

which method do you propose me to use with maple? (I don't mine about which boundary conditions to be used here).

 

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