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Modelling pendulums in maple...

January 16 2014
2 5

I'm trying to model a simple pendulum. I have arrived at this code which gives me an animation of a point swinging.

To analyse the pendulum I want to plot a graph of phi against time, but do not know how to take readings from my animation to plot a graph with.

Thanks.

Change in formula when a certain y-value is reache...

January 13 2014
2 10

Hello,

I was wondering how (or what is the best way) to write a worksheet in which a change of formula is used when a certain value on the y-axis is reached.

So for example: if there is a mass-spring system with damping in it, I would like to change the value of the damping when the displacement/velocity/acceleration has reached a certain value.
So when I apply a force to the mass-spring system, and the acceleration for example is LOWER than 0.2 m/s^2 I use a value of X % damping, but when the value of the acceleration is HIGER than 0.2 m/s^2 I want to apply Y % damping. So in time the curve will increase (when low damping is used) and the curve will decrease (because high damping is used, because the y-value is higher than 0.2 m/s^2), and so on...

I hope somebody has a 'simple' idea. I know what I want to do, but I don't know how to put this down in a formula which I can write in Maple.

Greetings,
Frank

How to fit or approximate a complicated function b...

January 03 2014
1 7

Hi everyone,

I have a very complicated function y with only one independent variable x, and want to fit or approximate it by a simpler function, say polynomial. Many books or maple reference seem to tell how to fit a set of data instead of a given function. But the argument x in the function is assumed to be continuous other than discrete, so I don't know whether it is possible to express datax in form of x's range such as 0..1, and express datay in form of the function. After that , maybe I can fit the two created data sets by a polynomial function.

Or, does anyone have a better or more direct way to do the fitting linking two fucntions?

I am appreciated for your help.

Best,

GOODLUCK

Mapple 16 mathematical function...

December 29 2013
0 0

hello. before I used Mapple 15. But then Ive run Mapple 16 and now Ive a problem. I cant use this program. I open the program, everthing is in the rule, but if I want to write any mathemathical function, or a letter, such as- x or x+2, the program doest give any reaction. program only gives reaction the numbers.

Please, help me. (my english isnt very good, and I dont know Ive explained my opinion).

Lssolve- midpoint...

December 25 2013
0 8

Hi,

I get the error in the following code

restart:

gama1:=0.01:

zet:=0;
#phi0:=0.00789:
Phiavg:=0.02;
lambda:=0.01;
Ha:=1;

0
0.02
0.01
1
rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])*(1-Ha^2*u(eta))+((1/(eta)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta));
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(-2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)+k(eta)/k1[w]/(eta)*diff(T(eta),eta) ));
eq3:=diff(phi(eta),eta)+phi(eta)/(N[bt]*(1+gama1*T(eta))^2)*diff(T(eta),eta);
/  d   /  d         \\   mu1[w] (1 - u(eta))
|----- |----- u(eta)|| + -------------------
\ deta \ deta       //         mu(eta)

/             /  d           \\
|      mu_phi |----- phi(eta)||
| 1           \ deta         /| /  d         \
+ |--- + -----------------------| |----- u(eta)|
\eta           mu(eta)        / \ deta       /
/      /
|      |
/  d   /  d         \\     1    |      |  rho(eta) c(eta) u(eta)
|----- |----- T(eta)|| + ------ |k1[w] |- ----------------------
\ deta \ deta       //   k(eta) |      |         5000 p2
\      \

/  d           \
(a[k1] + 2 b[k1] phi(eta)) |----- phi(eta)|
\ deta         /
+ -------------------------------------------
2
1 + a[k1] phi1[w] + b[k1] phi1[w]

/  d         \\\
k(eta) |----- T(eta)|||
\ deta       /||
+ ---------------------||
k1[w] eta      ||
//
/  d         \
phi(eta) |----- T(eta)|
/  d           \            \ deta       /
|----- phi(eta)| + ------------------------
\ deta         /                          2
N[bt] (1 + 0.01 T(eta))
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,eq1):
eq2:=subs(phi(0)=phi0,eq2):
eq3:=subs(phi(0)=phi0,eq3):

#A somewhat speedier version uses the fact that you really need only compute 2 integrals not 3, since one of the integrals can be written as a linear combination of the other 2:
Q:=proc(pp2,fi0) local res,F0,F1,F2,a,INT0,INT10,B;
global Q1,Q2;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve(subs(p2=pp2,phi0=fi0,{eq1=0,eq2=0,eq3=0,u(1)=lambda/(phi(1)*rhop/rhobf+(1-phi(1)))*D(u)(1),D(u)(0)=0,phi(1)=phi0,T(1)=0,D(T)(1)=1}), numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
INT0:=evalf(Int((1-eta)*F0(eta),eta=0..1-zet));
INT10:=evalf(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet));
B:=(-cbf*rhobf+cp*rhop)*INT10+ rhobf*cbf*INT0;
a[1]:=2/(1-zet^2)*B-10000*pp2;
a[2]:=INT10/INT0-Phiavg;
Q1(_passed):=a[1];
Q2(_passed):=a[2];
if type(procname,indexed) then a[op(procname)] else a[1],a[2] end if
end proc;
#The result agrees very well with the fsolve result.
#Now I did use a better initial point. But if I start with the same as in fsolve I get the same result in just about 2 minutes, i.e. more than 20 times as fast as fsolve:

Q1:=proc(pp2,fi0) Q[1](_passed) end proc;
Q2:=proc(pp2,fi0) Q[2](_passed) end proc;
Optimization:-LSSolve([Q1,Q2],initialpoint=[6.5,exp(-1/N[bt])]);

proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
HFloat(6.5), HFloat(0.006737946999)

the error is :

Error, (in Optimization:-LSSolve) system is singular at left endpoint, use midpoint method instead

how can I fix it.

Thanks

Amir

Strange for...while loop behavior?...

December 24 2013
2 2

Or I didn't get something right? This is with Maple 16.02 on a Mac:

> for i from 1 to 10 while i<=5 do print(i) end do; #works all right
> for i from 1 to 10 while i>=5 do print(i) end do; #nothing shows up?

solving inequality...

December 23 2013
1 0

I'm trying to solve the following inequality:

ln(x+1)<x^2-1

but the solve command returns:

"Warning, solutions may have been lost"

Can someone help me?

Thank you.

Carmelita

logarithmic inequality...

December 23 2013
1 2

I'm trying to solve the following inequality:

ln(x+1)<x^2-1

but the solve command returns:

"Warning, solutions may have been lost"

Can someone halp me?

Thank you.

Carmelita

Why does Maple Crash?...

December 19 2013
0 0

When you use the slider without Do(%MathContainer1 = StandardError(Variance, R)):
everything works ok but when you add Do(%MathContainer1 = StandardError(Variance, R)):
Maple Crashes.....

Strange...

LL_102)_Covariance_M.mw

Standard errors of covariance matrix in Maple?...

December 19 2013
0 1

How can I get the Standard Errors of the covariance matrix in Maple?
I can simulate a covariance matrix in Maple as follows:

restart:
with(Statistics):
with(LinearAlgebra):

R := RandomMatrix(4, 4, generator = -15 .. 15, outputoptions = [datatype = float[8]]);
CovarianceMatrix(R);

but how do I find the standard errors?

Error, invalid input: eval received params, which ...

December 13 2013
1 3

I write this system but I have 2 error

restart; params := [z = 0,

Omega = 2.2758,

tau = 13.8, T2 = 200,

omega0 = 1,

r = .7071,

s = 2.2758,

omega = .5]

sys1 := {diff(q(t), t) = -2*Omega*v(t)-s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*(y(t)-x(t))-q(t)/T2,

diff(v(t), t) = Omega*q(t)-v(t)/T2,

diff(x(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)+y(t)/T1,

diff(y(t), t) = -2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)-y(t)/T1};

ICs1 := {q(-20) = 0, v(-20) = 0, x(-20) = 1, y(-20) = 0}

ans1 := dsolve(union`(eval(sys1, params), ICs1), numeric, output = listprocedure); plots:-odeplot(ans1, [[t, x(t)], [t, y(t)], [t, q(t)], [t, v(t)]], t = -20 .. 20, legend = [x, y, q, v])

Error, invalid input: eval received params, which is not valid for its 2nd argument, eqns
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

solve system of differential equations numerically...

December 11 2013
0 0

Hello everybody

I'm new at using Maple

so what I'm trying to do is " solve system of differential equations numerically " and plot the result

I use the floweing code

PDEtools[declare]((u, v, w)(t), prime = t)

> params := z = 0;

Omega= 2.2758;

tau = 13.8;

T2 = 200; s = 1;

r = 0.7071;

\[CapitalDelta] = 1.7758;

s = 2.2758;

Eta= 1.05457173*10^-34;

omega = 0.5; k = 1666666.667;

> sys1 := {diff(u(t), t) = Omega*v(t)-u(t)/T2,

diff(v(t), t) = -Omega*u*{t}-2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*w(t)-v(t)/T2,

diff(w(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*v(t)};

Cs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

> ans1 := dsolve*RealRange(Open({ICs1, sys1}), {u(t), v(t), w(t)});
%;
Error, (in RealRange) invalid arguments

plot([u(t),t=-20..20])
plot([v(t),t=-20..20])
plot([w(t),t=-20..20])

:::::::::

also I need to use the result of v(t) in another equation as,

x=2*v(t)*cos(k*z-omega*t)

How I can do that ?

solve system of differential equations numerically...

December 11 2013
1 6

Hello everybody

I'm new at using Maple

so what I'm trying to do is " solve system of differential equations numerically " and plot the result

I use the floweing code

PDEtools[declare]((u, v, w)(t), prime = t)

> params := z = 0;

Omega= 2.2758;

tau = 13.8;

T2 = 200; s = 1;

r = 0.7071;

\[CapitalDelta] = 1.7758;

s = 2.2758;

Eta= 1.05457173*10^-34;

omega = 0.5; k = 1666666.667;

> sys1 := {diff(u(t), t) = Omega*v(t)-u(t)/T2,

diff(v(t), t) = -Omega*u*{t}-2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*w(t)-v(t)/T2,

diff(w(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*v(t)};

Cs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

> ans1 := dsolve*RealRange(Open({ICs1, sys1}), {u(t), v(t), w(t)});
%;
Error, (in RealRange) invalid arguments

plot([u(t),t=-20..20])
plot([v(t),t=-20..20])
plot([w(t),t=-20..20])

:::::::::

also I need to use the result of v(t) in another equation as,

x=2*v(t)*cos(k*z-omega*t)

How I can do that ?

December 08 2013
1 5

abs not differentiable at non-real arguments ...

December 05 2013
0 2

Hi There,

Can any one correct me the mistake in the following differentiation:

Above command gives the following error:

Error, (in simpl/abs) abs is not differentiable at non-real arguments

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