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Hi,

Here is my question.


restart

convert(diff(lambda(t-t1), t), diff)

eval(diff(lambda(t2), t2), {t2 = t-t1})

(1)

subs(lamda(t-t1) = sin(t-t1), %)

eval(diff(lambda(t2), t2), {t2 = t-t1})

(2)

``

I am trying to substitute value of lambda(t-t1) further but it is not taking the value.

Thanks in advance.

Regards

Sunit

Download question2.mw

hi

maple with collocation and galerkin methods

please help me with writing the cods

 

Hello everyone,

I have a problem with my  code, breif this is the equation that I want to solve 

x^2*(diff(y(x), x, x))+50*x*(diff(y(x), x))-35*y(x) = (1-exp(x+1))/(x+1)+(x^2+50*x-35)*exp(x)+int(exp(xt)*y(t), t = 0 .. 1), x = 0 .. 1

but the problem is that I don't know how to code the integral please guys help me 

Also always i try to solve that strange ecuation maple give me like an aswer in terms of Z, with an integral on it, i don't get nothing. I evaluate a point with right click, evaluate a point. Choose the variables value, and the time at wich i want to evaluate the ecuation. Later it give me the same strange solution but with the variables replaced for the values i gave to the program. Then i choose right click, aproximate, and don't matter if i select 5, 10 or more digits, it launchs to me the same strange ecuation, not the number i'm waiting for.

So that i want to know now is how can i manipulate a numerical solution to a diff ecuation.

For example if i got this system of diff ecuation

dx/dt = (-k/m) (x srqt(x^2 + y^2))

dy/dt = (-k/m) (y srqt(x^2 + y^2)) - g

Which is a projectile trajectory taking care of air drag force, and i want to know at which initial speed i have to fire the body to reach 300m if it is fired from the initial point at (0,0), and it's initial velocity on x is 3 times it's initial velocity on y (initial launch angle condition)? 

How can i input that conditions to make maple give me a solution for something like that?

Hi, i got this diff ecuation to answer. It is an ecuation of a proyectile, it give the angle of speed with respect to time. I typed it on wolfram; got an aswer. When i tried on maple without any initial condition, got a good answer. With an initial condition, didn't get nothing. I even tried with the interactive solver, got a 'can't solve'. So this is my ecuation:

dx/dt = -[g cos(x)] / [vo - g t sin(x)]

I had to find the initial coindition for myself after that, i supect what the problem is. Maple gave an aswer in terms of arctan (y,x), and i think, based on my own try, it doesn't know how to find a term if it's inside the arctan function, typed in that way. So i rewrited it like arctan (y/x), anf found my constant C1.

 

Another problem i got was about this system of diff ecuations:

dx/dt = (-k/m) (x srqt(x^2 + y^2))

dy/dt = (-k/m) (y srqt(x^2 + y^2))

Again was wolfram who gave me a good answer to the problem. So you are going to understand im thinking wolfram is better on symbolic calculation. Thanks anyway for your help and effort.

 

 

 

 

Hello,

 

I'm modeling the simple DC motor system in Maple.
The equations describing the system;

eq1:=J*diff(theta(t),t,t)+b*diff(theta(t),t)=K*i(t):
eq2:=L*diff(i(t),t)+R*i(t)=V(t)-K*diff(theta(t),t):
DCMotor:=[eq1,eq2];

First, I create the system using DiffEquation:

Sys:=DiffEquation(DCMotor,[V(t)],[theta(t)]);

And now I have problem. The input var is V(t) (input voltage) and the output var is theta(t) (position of the rotor).

But I wont to have in output var not position of the rotor but speed of the fotor - diff(theta(t),t)

How to set output var for diff(theta(t),t) (the speed of the motor)?

 

Best

Rariusz

 

Dear all.

I am a french ingineering student and I have some problems trying to modelize the ascension of a space balloon (closed balloon full of Helium) from 0 to 11000m in ISA conditions.

I think that my initialization is OK but I'm unfortunately not able to find how to solve my non linear equation. My equation is: ` ρ`[air]*V[Ballon]*g = mg+(1/2)*rho[air]*C[x]*V[z]^2

I copy my work below:

###############################################################################

#Atmospheric parameters, initialization
#temperature (K)

Ta := 15-6.5*((1/1000)*z(t))+273.15;

#pressure (Pascal)

 

 Pa := 1013*10^2*(1-3.32*10^(-5)*z(t))^(7/2);

#moleculai mass of air

 

M := 29;

#thermodynamic constant

R := 8.314;

#volumic mass of air following the altitude

 

J := M*Pa/(R*Ta);

#Laplace coefficient, initial volume of the balloon, ground pressure:

 

ga := 1.6665;

V0 := 4.43;

P0 := 1.013*10^2;

#Balloon volume following the altitude (Laplace formula)

 

Vball1 := (P0/Pa)^(1/ga)*V0;

#Disc surface for the drag force

S1 := 3.14^(1/3)*(3/4)^(2/3)*Vball1^(2/3);

with(DEtools);

Cx := .44; #(turbulent flow)

g := 9.81;

mball := 3; #(balloon mass)

ode1 := J*Vball1*g-mball*g-(1/2)*J*S1*Cx*(diff(z(t), t))^2 = 0;

ics := (D(z))(0) = 0, z(0) = 0:

dsolve(????????);

###############################################################################

The problem is that because of its non linear aspect, i don't know what kind of method I have to use to find the solution with my initial conditions. 

Thank you in advance for your answer, 

ANTHONY 

Hello

I am new to Maple. I am solving the differential equation with the given initial condition. I am getting some error. Can anyone help me please.

 

Thanks

maple_help.mw

This procedure calculate the equations of motions for Euclidean space and Minkowski space  with help of the Jacobian matrix.

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

"EQM := proc(eq, g,xup,xa,xu , eta ,var)"

Calling Sequence

 

EQM(eq, g, xup, xa, xu, eta, var)

Parameters

 

parameterSequence

-

eq, g, xup, xa, xu, eta, var

eq

out

equation of motion

g

out

metric

xup

out

velocitiy vector

xa

in

position vector

xu

in

vector of the independet coortinates

eta

in

signature matrix for Minkowski space

var

in

independet variable

 

``

 Procedur Code

 

restart; with(linalg); EQM := proc (eq, g, xup, xa, xu, eta, var) local J, Jp, xdd, l, xupp, ndim; ndim := vectdim(xu); xup := vector(ndim); xupp := vector(ndim); for l to ndim do xup[l] := diff(xu[l](var), var); xupp[l] := diff(diff(xu[l](var), var), var) end do; J := jacobian(xa, xu); g := multiply(transpose(J), eta, J); g := map(simplify, g); Jp := jacobian(multiply(J, xup), xu); Jp := map(simplify, Jp); xdd := multiply(inverse(g), transpose(J), eta, Jp, xup); xdd := map(simplify, xdd); xdd := map(convert, xdd, diff); eq := vector(vectdim(xupp)); for l to ndim do eq[l] := xupp[l]+xdd[l] = 0 end do end proc

``

Input

 

xa := Vector(3, {(1) = R*sin(`ϕ`)*cos(`ϑ`), (2) = R*sin(`ϕ`)*sin(`ϑ`), (3) = R*cos(`ϕ`)}); xu := Vector(2, {(1) = `ϕ`, (2) = `ϑ`}); eta := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

 

EQM(eq, g, xup, xa, xu, eta, t):

Output EOM

 

for i to vectdim(xu) do eq[i] end do;

diff(diff(`ϕ`(t), t), t)-cos(`ϕ`)*sin(`ϕ`)*(diff(`ϑ`(t), t))^2 = 0

 

diff(diff(`ϑ`(t), t), t)+2*cos(`ϕ`)*(diff(`ϑ`(t), t))*(diff(`ϕ`(t), t))/sin(`ϕ`) = 0

(5.1)

Output Line-Element

 

ds2 := expand(multiply(transpose(xup), g, xup));

(diff(`ϕ`(t), t))^2*R^2+(diff(`ϑ`(t), t))^2*R^2-(diff(`ϑ`(t), t))^2*R^2*cos(`ϕ`)^2

(6.1)

Output Metric

 

assume(cos(`ϕ`)^2 = 1-sin(`ϕ`)^2); g := map(simplify, g)

array( 1 .. 2, 1 .. 2, [( 2, 2 ) = (R^2*sin(`ϕ`)^2), ( 1, 2 ) = (0), ( 2, 1 ) = (0), ( 1, 1 ) = (R^2)  ] )

(7.1)

``

``

 

Download bsp_jacobi.mw

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

"EQM := proc(eq, g,xup,xa,xu , eta ,var)"

Calling Sequence

 

EQM(eq, g, xup, xa, xu, eta, var)

Parameters

 

parameterSequence

-

eq, g, xup, xa, xu, eta, var

eq

out

equation of motion

g

out

metric

xup

out

velocitiy vector

xa

in

position vector

xu

in

vector of the independet coortinates

eta

in

signature matrix for Minkowski space

var

in

independet variable

 

``

 Procedur Code

 

restart; with(linalg); EQM := proc (eq, g, xup, xa, xu, eta, var) local J, Jp, xdd, l, xupp, ndim; ndim := vectdim(xu); xup := vector(ndim); xupp := vector(ndim); for l to ndim do xup[l] := diff(xu[l](var), var); xupp[l] := diff(diff(xu[l](var), var), var) end do; J := jacobian(xa, xu); g := multiply(transpose(J), eta, J); g := map(simplify, g); Jp := jacobian(multiply(J, xup), xu); Jp := map(simplify, Jp); xdd := multiply(inverse(g), transpose(J), eta, Jp, xup); xdd := map(simplify, xdd); xdd := map(convert, xdd, diff); eq := vector(vectdim(xupp)); for l to ndim do eq[l] := xupp[l]+xdd[l] = 0 end do end proc

``

Input

 

t := x[0]/c; xa := Vector(4, {(1) = t, (2) = r*cos(`ϕ`), (3) = r*sin(`ϕ`), (4) = x[3]}); xu := Vector(4, {(1) = x[0], (2) = r, (3) = `ϕ`, (4) = x[3]}); eta := Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1})

 

EQM(eq, g, xup, xa, xu, eta, tau):

Output EOM

 

for i to vectdim(xu) do eq[i] end do;

diff(diff(x[0](tau), tau), tau) = 0

 

diff(diff(r(tau), tau), tau)-(diff(`ϕ`(tau), tau))^2*r = 0

 

diff(diff(`ϕ`(tau), tau), tau)+2*(diff(`ϕ`(tau), tau))*(diff(r(tau), tau))/r = 0

 

diff(diff(x[3](tau), tau), tau) = 0

(5.1)

Output Line-Element

 

ds2 := expand(multiply(transpose(xup), g, xup));

-(diff(x[0](tau), tau))^2/c^2+(diff(r(tau), tau))^2+(diff(`ϕ`(tau), tau))^2*r^2+(diff(x[3](tau), tau))^2

(6.1)

Output Metric

 

assume(cos(`ϕ`)^2 = 1-sin(`ϕ`)^2); g := map(simplify, g)

array( 1 .. 4, 1 .. 4, [( 3, 3 ) = (r^2), ( 3, 4 ) = (0), ( 4, 1 ) = (0), ( 1, 1 ) = (-1/c^2), ( 4, 3 ) = (0), ( 4, 2 ) = (0), ( 2, 2 ) = (1), ( 3, 2 ) = (0), ( 3, 1 ) = (0), ( 2, 4 ) = (0), ( 1, 4 ) = (0), ( 1, 2 ) = (0), ( 2, 3 ) = (0), ( 4, 4 ) = (1), ( 2, 1 ) = (0), ( 1, 3 ) = (0)  ] )

(7.1)

``

``

 

Download bsp_jacobi_minkowski.mw

how to transform this differential equation with a substitution?

f := diff(u(x),x$2) + p(x)*diff(u(x),x)+q(x)*u(x)=0;
transformed := subs(x=1/t, f);

 

f := diff(u(x),t$2)*diff(t,x$2) + p(x)*diff(u(x),t)*diff(t,x)+q(x)*u(x)=0;

diff(1/t,t);
diff(1/t,t$2);

 

x = 1/t
dx/dt = -1/t^2
d2x/dt2 = 2/t^3

d2u/dt2*dt2/dx2
du/dt*dt/dx
diff(u(t),t$2)*1/(2/t^3) + p(t)*diff(u(t),t)*1/(-1/t^2)+q(t)*u(t)

restart;
f := u2*1/(2/t^3) + p(t)*u1*1/(-1/t^2)+q(t)*u;
f2 := collect(f/t^3*2, {u2, u1, u});
subs(u2 = diff(u(t),t$2), subs(u1 = diff(u(t), t), subs(u=u(t), f2)));

but not equal to below which is in book, is this equation wrong in book?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;

 

Hi everyone--my differential equations course is using Maple; this is my first time using the program and I am a little cofused. 

In a lab component we are told to take the differential equation " dy/dx = sin (x - y) " and substitute in y = ax+b, then determine which coeffecients of a and b should be in order to obtain a solution.

I have made many attemps at this substitution, but am encountering syntax errors no matter what I do:

http://imgur.com/WVQsUQy

 

I know the general equation would be written in Maple as

 

>

 

..which presents no problems for me, format-wise, and generates a nice output.

However, any iteration I've tried with substituting y = ax+ b has resulted in an error like those shown in the linked image above; I'd really appreciate it if someone could explain how I would do the substitution and maybe what I'm doing wrong, syntax-wise.

 

Thank you for your time!

Dear friends,

 

I have a huge differential equation which I am trying to solve.

However, even solving it numerically, maple keeps evaluating it for a long time and then stops working! So there is no solution.

I just want to check if there is any solution to this differential equation at all!

Do you know a way with which maple can check if the differential equation is solvable?

 

I am interested in dynamic systems that changes system equations at a given point in time. So i often want to plot graphs that shows what would happen in the first 500 seconds, then using the point reached after 500 seconds as the starting point show what happens over the next 500 seconds.

For example my equations might innitially

diff(x,t)=x+p*y

diff(y,t)=x/y

and then after 500 seconds switch to 

diff(x,t)=x-p*y

diff(y,t)=x/y

simply estimating where the system is and feeding that into the other equation isn't an option because these equations have lots of parameters which p is representing in the above, and generally i want too use these graphs to illustrate the behaveious of the systems with the given parameters.

So far i use display and DEplot to make these grpahs.

Non dimensionalisation is a vary common task, and I was suprised that I couldn't find a maple tool to automate it . Has anyone developed their own package for it?

I want to automatically do it to the system equations for some Dynamical systems to make some of the other processing I do with them easier.

I was hoping to start with somehting in the form of 

Diff(x[1],t)=f[1](p[1]....p[n],x[1]...x[m])

...

Diff(x[m],t)=f[m](p[1]....p[n],x[1]...x[m])

where each f[i] is some kind of quotient of multivariate polynomials in the variables and parameters:
and end up with something like

Diff(y[1],s)=f[1](q[1]....q[p],y[1]...y[m])

...

Diff(y[m],s)=f[m](q[1]....q[p],y[1]...y[m])

where p<n


 

Download inf2.mw

hello

 

i write this set of differential equation in maple and get the following error?

Can anyon help me with this?

 

thanks

 

 

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