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ex4_lista_CSTR.mw

Variáveis

 

``

restart;

F[A][0] := 43, 4;

43, 4

 

802, 8

 

0

 

71, 87

(1.1)

C[P][A] := 35;

35

 

18

 

46

 

19, 5

(1.2)

deltaC[P] := -C[P][A]-C[P][B]+C[P][C];

-7

(1.3)

V := 40, 1

40, 1

(1.4)

v[A][0] := 46, 62;

46, 62

 

46, 62

 

233, 1

(1.5)

v[0] := v[A][0]+v[M][0]+v[B][0];

325, 125

(1.6)

H[A][ref] := -66600;

-66600

 

-123000

 

-226000

(1.7)

deltaH[R][ref] := -H[A][ref]-H[B][ref]+H[C][ref];

-36400

(1.8)

deltaH[R] := deltaH[R][ref]+deltaC[P]*(T-T[ref]);

-36400-7*T+7*T[ref]

(1.9)

``

k := 16, 96*10^12*exp(-32400/(R_*T));

16, 96000000000000*exp(-32400/(R_*T))

(1.10)

R_ := 1, 987;

1, 987

(1.11)

C[A][0] := F[A][0]/v[0];

(43, 4)/(325, 125)

(1.12)

T[0] := 75;

75

(1.13)

T[ref] := 68;

68

(1.14)

 

Balanço Molar

 

r[A] := -k*C[A][0]*(1-X[MA](T));

-(16, 96000000000000*exp(-32400/((1, 987)*T)))*(43, 4)*(1-X[MA](T))/(325, 125)

(2.1)

``

EQ1 := X[MA](T) = V*k/(V*k+v[0]);

X[MA](T) = (40, 1)*(16, 96000000000000*exp(-32400/((1, 987)*T)))/((40, 1)*(16, 96000000000000*exp(-32400/((1, 987)*T)))+(325, 125))

(2.2)

``

Balanço de Energia

 

r[A] := -k*C[A][0]*(1-X[EA](T));

-(16, 96000000000000*exp(-32400/((1, 987)*T)))*(43, 4)*(1-X[EA](T))/(325, 125)

(3.1)

``

EQ2 := X[EA](T) = 1-(C[P][A]*F[A][0]+C[P][B]*F[B][0]+C[P][C]*F[C][0])*(T-T[0])/(deltaH[R]*V*k*C[A][0]);

X[EA](T) = 1-(15941, 284)*(T-75)*(325, 125)/((-35924-7*T)*(40, 1)*(16, 96000000000000*exp(-32400/((1, 987)*T)))*(43, 4))

(3.2)

``

``



Download ex4_lista_CSTR.mw

 

Just got Maple 18 on academic license. I've used Maple 15, 16 and 17 before this.

It wont write simple math symbols as + - * and := 

I have tried both document- and worksheet, reinstalling and so on...

 

What is the problem?

Thanks

Hi. It is be good to be with you after 4 years.

I want to ask about Curvefitting for Data. If I have a numerical data and i want to find a function in x and y for these data.

Hi,

I was wondering how I could assign small angel assumptions so that I could simplify an equation of motion to solve for theta double dot. Thank you for your help.


Download small_angle_assumption.mw

Equation Manipulation

-assumptions- small angel

"sin(`ϑ`):=`ϑ`"

`ϑ`

(1)

"cos(`ϑ`):=1"

1

(2)

diff(`ϑ`(t), t) := 0

NULL

diff(x(t), t, t) := (H+u)/M


I*(diff(`ϑ`(t), t, t)) = [m*(-l*(diff(`ϑ`(t), t))^2*cos(`ϑ`)-l*(diff(`ϑ`(t), t, t))*sin(diff(`ϑ`(t), t)))-m*g]*l*sin(`ϑ`)+[m*(l*(diff(`ϑ`(t), t))^2*sin(`ϑ`)-l*(diff(`ϑ`(t), t, t))*cos(diff(`ϑ`(t), t))+diff(x(t), t, t))]*l*cos(`ϑ`)

"(->)"

Error, (in isolate) unable to isolate diff(diff(`ϑ`(t), t), t)

 

NULL

``


Download small_angle_assumption.mw

After taking the inverse Laplace transform of a function, I wrote a Maple command to evaluate the result at some specified values of t (for example at t=0), it returned solution in equation (2) . I expected single numerical value for each value of t, but , it gave the result in form of  linear combinations of  delta(2,0), delta(3,0), delta(4,0), etc. See below:

> restart;
> with(Physics);
> Setup(mathematicalnotation = true); complex*number;
[mathematicalnotation = true]
complex number
> k[1] := 139.39; c[1] := .2725; mu[1] := 5.9410; gamm1 := 2;
> P[0] := 1; M := 70; g := 9.8; v := 6.5; L := 6;
> P1 := P[0]*M*g*(-L*s/v)^k/factorial(k);
> Y[1](0), Y[1](1), Y[1](2), Y[1](3) := 0., a, 0., c;
> Y[2](0), Y[2](1), Y[2](2), Y[2](3) := 0., b, 0., d;
> B[k-r] := KroneckerDelta[k, r]-(3/2)*KroneckerDelta[k, r+1]+(3/4)*KroneckerDelta[k, r+2]-(1/8)*KroneckerDelta[k, r+3];
> B1 := -(3/2)*KroneckerDelta[k, r]+(3/2)*KroneckerDelta[k, r+1]-(3/8)*KroneckerDelta[k, r+2];
> B2 := (3/2)*KroneckerDelta[k, r]-(3/4)*KroneckerDelta[k, r+1];
> Q[k-r] := KroneckerDelta[k, r]-(1/2)*KroneckerDelta[k, r+1];
> A1 := sum(B[k-r]*(r+1)*(r+2)*(r+3)*(r+4)*Y[1](r+4), r = 0 .. k)+2*(sum(B1*(r+1)*(r+2)*(r+3)*Y[1](r+3), r = 0 .. k))+sum(B2*(r+1)*(r+2)*Y[1](r+2), r = 0 .. k)+k[1]*(Y[1](k)-Y[2](k))+c[1]*s*(Y[1](k)-Y[2](k))-mu[1]*s*(k+1)*(k+2)*(Y[1](k+2)-Y[2](k+2))+sum(gamm1*s^2*Q[k-r]*Y[1](r), r = 0 .. k) = P1;
> A2 := sum(B[k-r]*(r+1)*(r+2)*(r+3)*(r+4)*Y[2](r+4), r = 0 .. k)+2*(sum(B1*(r+1)*(r+2)*(r+3)*Y[2](r+3), r = 0 .. k))+sum(B2*(r+1)*(r+2)*Y[2](r+2), r = 0 .. k)+k[1]*(Y[2](k)-Y[1](k))+c[1]*s*(Y[2](k)-Y[1](k))-mu[1]*s*(k+1)*(k+2)*(Y[2](k+2)-Y[1](k+2))+sum(gamm1*s^2*Q[k-r]*Y[2](r), r = 0 .. k) = 0;
> m := 12;
> for i from 0 to m do Y[1](i+4) := collect(solve(eval(A1, k = i), Y[1](i+4)), {a, b, c, d}); Y[2](i+4) := collect(solve(eval(A2, k = i), Y[2](i+4)), {a, b, c, d}) end do;
>
> A3 := sum(Y[1](k), k = 0 .. 8) = 0;
> A4 := sum(k*(k-1)*Y[1](k), k = 0 .. 8) = 0;
> A5 := sum(Y[2](k), k = 0 .. 8) = 0;
> A6 := sum(k*(k-1)*Y[2](k), k = 0 .. 8) = 0;
> sol := solve({A3, A4, A5, A6}, {a, b, c, d});
> Y[1] := eval(sum(Y[1](k)*xi^k, k = 0 .. 8), sol);
>
> with(inttrans);
> y[1] := invlaplace(Y[1], s, t);
> y[2] := subs(I = 0, y[1]);

>
> for xi from 0 by .1 to 1 do y[xi] := eval(eval(y[2], {t = 0})) end do;
y[0] := 0.
y[0.1] := -335.8210943 - 0.2853134161 delta(1, 0)

- 0.003189135039 delta(2, 0) + 3.215933203 delta(0)

-8 -9
- 2.101888941 10 delta(3, 0) + 8.278917357 10 delta(4, 0)
y[0.2] := -616.5812812 - 0.7286587659 delta(1, 0)

+ 0.003338719654 delta(2, 0) + 2.597336701 delta(0)

-7
- 0.000001136393191 delta(3, 0) + 2.587772223 10 delta(4, 0)
y[0.3] := -787.6445525 - 1.474810997 delta(1, 0)

+ 0.02853884261 delta(2, 0) - 5.517159103 delta(0)

- 0.00001031142443 delta(3, 0) + 0.000001812552944 delta(4, 0)
y[0.4] := -811.1848471 - 2.589947077 delta(1, 0)

+ 0.07684191276 delta(2, 0) - 23.27219517 delta(0)

- 0.00004426296248 delta(3, 0) + 0.000006660566248 delta(4, 0)
y[0.5] := -682.8521581 - 3.984266525 delta(1, 0)

+ 0.1440502970 delta(2, 0) - 49.60730104 delta(0)

- 0.0001229043255 delta(3, 0) + 0.00001666149585 delta(4, 0)
y[0.6] := -441.5562325 - 5.350681306 delta(1, 0)

+ 0.2144868917 delta(2, 0) - 78.78970103 delta(0)

- 0.0002502887215 delta(3, 0) + 0.00003148839539 delta(4, 0)
y[0.7] := -167.0511892 - 6.158350095 delta(1, 0)

+ 0.2612340304 delta(2, 0) - 100.0143657 delta(0)

- 0.0003906180172 delta(3, 0) + 0.00004649544839 delta(4, 0)
y[0.8] := 39.3465739 - 5.754055618 delta(1, 0)

+ 0.2517612354 delta(2, 0) - 99.27848038 delta(0)

- 0.0004565738656 delta(3, 0) + 0.00005214660880 delta(4, 0)
y[0.9] := 94.9253902 - 3.638647825 delta(1, 0)

+ 0.1617018641 delta(2, 0) - 65.09861522 delta(0)

- 0.0003369182899 delta(3, 0) + 0.00003737844304 delta(4, 0)
-7
y[1.0] := -0.00034023 + 5.342230828 10 delta(1, 0)

-8
- 2.395810153 10 delta(2, 0) + 0.000005214637385 delta(0)

-9 -11
- 1.077399852 10 delta(3, 0) + 1.681923081 10 delta(4, 0)

I am sure that with this vector file with embedded components will learn how it works the vector operations. The code is free and can be modified to be improved. Forward engineers.

 

Vectores_con_Components_Embedded.mw     (in spanish)      

 

Lenin Araujo Castillo

I typed (x-a)(x-a) into Maple 18 (the only thing in a new document) and got x(x-a)-a 

I'm wondering why it is evaulated like this?

Is this because of a setting?

BTW, I evaluated at a=4 first. 

How do you use algcurves and Puiseux series in Maple?

Hi,

I am trying to plot only the real part of the values obtained from the MapleSim model.  Probably there is a Modelica function to get only the real part of the values, but I am unable to find it. Could you please have a look at the code and let me know what I should do to solve this problem?

Best

Onder

 

The code is: (I want to plot the real part of R2)

 

model IKTest

parameter Boolean switched = false;
parameter Modelica.SIunits.Length L1 = 0.100;
parameter Modelica.SIunits.Length L2 = 0.102;
parameter Modelica.SIunits.Length L3 = 0.5;
//parameter Real c; //Complex number
//parameter c;

Modelica.Blocks.Interfaces.RealInput u[3]
annotation (Placement(transformation(extent={{-140,-20},{-100,20}},rotation=0)));
Modelica.Blocks.Interfaces.RealOutput y[3]
annotation (Placement(transformation(extent={{90,-10},{110,10}},rotation=0)));

Real Tx = u[1];
Real Ty = u[2];
Real Tz = u[3];
Real R1 = y[1];
Real R2 = y[2];
Real R3 = y[3];

equation

R1=atan(Ty/Tz);
R2=(acos((L1^2+L2^2-(sqrt(Tx^2+Ty^2+Tz^2))^2)/(2*L1*L2)));

//2*Modelica.Math.asin(1.0)
//R3=R2.re;

annotation (uses(Modelica(version = "3.1")));
end IKTest;

I'm taking my first steps with maple and pdsolve, trying to run the example in the maplesoft support page:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/pdsolve_boundaryconditions

which reads

>
> restart; with(PDEtools);
> U := diff_table(u(x, t));
>

and I get a solution that is different from the web page, and when i run

Im using maple 13. Any tips about what's wrong?

 

regards

Hi there

I'm working with maple 13 (2d input) and I would like to hide the input in a worksheet, as follows:

view > show/hide contents > (unchecking) input

however i want to insert comments as text that will remain in my worksheet. Using '#' doesn't help, coz they get hidden too.

Couldn't sort out how to do this, any tips?

cheers

Hi there

I'm taking my first steps with maple and my question is not exactly briliiant

Putting in a simple way, I'm trying to solve sth that looks like this

> li := a*[cos(7*x+8*x*y+9*y)*cos(-7*x-8*x*y-9*y)];
             a [cos(7 x + 8 x y + 9 y) cos(-7 x - 8 x y - 9 y)]

and i want to replace

with

getting (if i do it by hand)

> algsubs(7*x+8*x*y+9*y = 20*y, li);
                    a [cos(20 y) cos(-7 x - 8 x y - 9 y)]

my question, is there an elegant way to do it? sth that would look like this?

 

 

thank you for any tips

Hi There

I'm getting started with maple and facing a doubt about using subs, somehow it does not seem to work, this is my expression:

 

> restart;
> theta := omega*t-k*x;
                                omega t - k x
> phi[1] := -(1/2)*H*c*cosh(k*(z+h))*sin(theta)/sinh(k*h);
                   H c cosh(k (z + h)) sin(-omega t + k x)
                   ---------------------------------------
                                 2 sinh(k h)              
> diff(phi[1], t, t);
                                                             2
                H c cosh(k (z + h)) sin(-omega t + k x) omega
              - ----------------------------------------------
                                 2 sinh(k h)                  
> td := simplify(subs(z = 0, %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
> simplify(subs(cosh(k*h)/sinh(k*h) = 1/tanh(k*h), %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
I cannot subs cosh/sinh = tanh. I would like to know why.

Any tips? Thank you

The Interactive Embedded Components in Physics are of great importance today and will be even more in the future. Hereand leave a small tutorial of Embedded Components in Physics applied to physics. I hope that somehow you motives to continue the development of science.

 

  Interactive_Embedded_Components_in_Physics.mw      (in spanish)                 

 

Atte.

Lenin Araujo Castillo

Physics Pure

Computer Science

 

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