emersondiaz

Plot a vector field...

Asked: emersondiaz 55 Product: Maple 2024

May 07 2024

1 1

Good day to all of you nice people.
I'm currently attempting to plot a vector field where each component of the vector is defined by the equations S_x, S_y, and S_z, which are functions of the radial coordinate. Here is a depiction of how the vectors change with respect to r:

The next step, which I'm unsure how to do, is to plot the vectors around the z-direction, or I should say, in phi direction, to achieve something similar to this example:

Thank you a lot for your kind help.

Here is my code:
Maple_Question.mw

How can I get solution of this integral?...

Asked: emersondiaz 55 Product: Maple 2023

February 27 2024

0 0

Good day to all of you friends, just asking for your kind help.

I have been trying to get solution of the next integral but didn't have succes. The goal of the code is to perfom a variable change.

Best regards

$r := simplify(rhs(isolate(r+(2*M*`r__\`+\``+a*m/sigma)*log[10](r/`r__\`+\``-1)/(`r__\`+\``-`r__-`)-(2*M*`r__-`+a*m/sigma)*log[10](r/`r__-`-1)/(`r__\`+\``-`r__-`) = `r__&lowast;`, r)))$

omega := sqrt(r^2+a^2+a*m/sigma)

F := simplify(Delta*lambda*m__p/(2*m__p^2*omega^2*r^2*sigma+2*lambda^2*omega^2*sigma))

Download maple_primes_question.mw

Problem with Taylor series...

Asked: emersondiaz 55 Product: Maple

February 15 2024

1 1

Good day people, here just asking for your help please.

I am trying to do a taylor serie of a function but I recieved this error:

Error, (in Typesetting:-NeedsBrace) invalid input: the 1st argument to pointto is not a valid pointer handle

The aim of this is get the series to do its integration.

Thank you a lot for your responses.

maple_primes_question.mw

Error: division by zero...

Asked: emersondiaz 55 Product: Maple 2023

November 21 2023

1 0

Good day to all of you.

I am working with a differential equation, got a first approximation setting all the constants equal to 1. But at the time to use the real values there appears the error numeric exception: division by zero.

I'll thanks any advice.

best regards

division_by_zero.mw

solution of differential equations...

Asked: emersondiaz 55 Product: Maple 2023

October 22 2023

1 4

Good day to all the members who read this question.
I ask for your help to find the right way to solve this two differential equations (is attached the file). Used the common code "dsolve" but is not working on this problem. Doesn't matter if the solution is numeric or algebraic.
I will thaks a lot your kind help.
Best regards to all of you

DIFFERENTIAL_EQUATION.mw

First Part

The differential equation to solve:

(Delta*LinearAlgebra:-Transpose(D[1/2])*D__0-I*`μ__e`*D__0/(lambda+I*`μ__e`*r)-2*(`μ__e`^2*r^2+lambda^2))*R(r)

Definitions

D__n = `&PartialD;__r`+I*omega(a^2+r^2)/Delta+I*a*m/Delta+2*n*(r-M)/Delta

LinearAlgebra:-Transpose(D[n]) = `&PartialD;__r`-I*omega(a^2+r^2)/Delta-I*a*m/Delta+2*n*(r-M)/Delta

I divided the differential equation in 3 parts (A, B, C).

A := (-I*omega(a^2+r^2)-I*a*m+r-M)*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)+Delta*(diff(R(r), r, r))+I*omega(a^2+r^2)*(diff(R(r), r))+I*a*m*(diff(R(r), r))

B := -I*`μ__e`*(diff(R(r), r)+I*omega(a^2+r^2)*R(r)/Delta+I*a*m*R(r)/Delta)/(lambda+I*`μ__e`*r)

$R(r) = DESol({diff(diff(_Y(r), r), r)-(1-r+I/(1+I*r))*(diff(_Y(r), r))/(r^2-2*r+1)-(-(2*I)*((-1-2*I)+r)/(r^2-2*r+1)-2/((1+I*r)*(r^2-2*r+1))+2*r^2+2)*_Y(r)/(r^2-2*r+1)}, {_Y(r)})$

(1)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

Second Part

The differential equation to solve:

$[`#msub(mi("L",fontweight = "bold"),mfrac(mn("1",fontweight = "bold"),mn("2",fontweight = "bold"),linethickness = "1"))`*LinearAlgebra:-Transpose(L[1/2])+a*`μ__e`*sin(theta)*LinearAlgebra:-Transpose(L[1/2])/(lambda+a*`μ__e`*cos(theta))+2*(lambda^2+a^2*`μ__e`*cos(theta)^2)]*S(theta) = 0$

Definitions:

Also I divided the differential equation in 3 parts (A, B, C).

F := (omega*a*sin(theta)+m/sin(theta)+1/(2*tan(theta)))(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))+diff(S(theta), theta, theta)-omega*a*sin(theta)*(diff(S(theta), theta))-m*(diff(S(theta), theta))/sin(theta)+(diff(S(theta), theta))/(2*tan(theta))

G := a*`μ__e`*sin(theta)*(diff(S(theta), theta)-omega*a*sin(theta)*S(theta)-m*S(theta)/sin(theta)+S(theta)/(2*tan(theta)))/(lambda+a*`μ__e`*cos(theta))