## How to apply Homotopy operator for inversion of di...

Suppose I have an expression like

Is it possible to reverse the divergence expression using homotopy operator to obtain Psi and Phi?

The above divergence expression is possible since Euler operator of the left side is zero.

## What is causing this error with InitialValueProble...

I'm trying to approximate the solution of an IVP using Euler's method in the InitialValueProblem command and I keep getting this error (see attached worksheet). Can someone explain why? Thanks!

## Konigsberg Graph?...

Hello I'm having trouble create Konigsberg Graph on Maple. Here's the picture. Sorry if it's not clear enough. Thanks!

## Eulers method plot ...

Hi,

The question:

Create a table of the droplet´s range as a funstion of the initial velcity for v0=0.2..4 m/s in steps of 0.2 m/s, each with starting angle of 36 degree. What range of Reynolds numbers does this correspond to? Plot the result.

I get the result for one of the v values, but struggling to get values for all the v-values.

F_D:=proc(v::list) #force/mass
local k,vx,vy;
vx:=v[1];
vy:=v[2];
k:=-evalf(3*Pi*mu*d/m);        #common constant, calculated only one time
[k*vx,k*vy];                           #returns a vektor
end proc;

Euler:=proc(vo::list,h)             #using the Euler method to solve the equations
local vx,vy, F;
F:=F_D(vo);
vx:=vo[1]+h*F[1];
vy:=vo[2]+h*(F[2]-g);
[vx,vy];
end proc;

## Euler's Method on Aircraft...

Hi, I am working on an assignment and I am having difficulties with this Eurler method since I am working with vector.

The assignment:

If the aircraft's engine transmits power P to the air, the force of the propellar, Fp, satisfies P=Fpv. Since the force Fp acts in the direction of motion, it can be written in vector form as: (what I have so far)

with(linalg);

v:=Vector(2,1,[vx,vy]); velocity vector

nu:=v->Norm(Vector(v),2); (length of v)

Fd:=-1/2*C*rho*A*nu*v # air resistance

Fl:=1/2*Cl*rho*A*nu*v # liftforce in y direction here v=[-vy,vx]

Fp:=(P/nu^2)*v^2 # power from aircraft

F_T:=v->Vector(evalm(Fp/nu(v)^2*v+Fd*nu(v)*v+Fl*nu(v)*zip((x,y)->x*y,v([2,1]),Vector([-1,1]))+Vector(2,1,[0,-m*g]))); # I have tried it and it works

so up til here I am good. It is this next part that I can't seam to get.

Write a routine which uses Euler's method to solve the equation of motion numerically for velocity v(t):

m*dv/dt=F_T(v)

Test the program by trying a plane with intitial velocity [v0,0] such that it maintains this speed when the engines power is P=P0

We have been given an Esolve we can use:

Esolve:=proc(f::procedure,h,x0,y0,N::integer) # Calculates y(x0+n*h) for n=1..N given y0=y(x0) and f(x,y)

local n,y,x;

y[0]:=y0; # Start Value
x:=x0;

for n from 1 to N do
y[n]:= y[n-1]+h*f(y[n-1],x); # Euler's formula
x:=x+h; # Next x
end do;

y;

end proc;

If anyone could help me understand how it works and how to get this to work with vectors I would be very gratefull.

## Difference between Inboard frame and Euler for the...

Hello,

In my mechanism, I use absolute coordinates.

For the rotation (namely the initial angles/ angular velocites), I didn't see the difference between Inboard and Euler.

It seems to me that in the two cases, the initial angles are defined with regard to the inertial frame and for both, different kind of rotations can be defined.

Have you some ideas on these two options ?

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
local no_points,x_old,x_new,y_old,y_new,i:
no_points:=round(evalf((xn-x0)/h)):
x_old:=x0:
y_old:=y0:

for i from 1 to no_points do
x_new:=x_old+h:
y_new:=y_old+evalf(h*f(x_old,y_old)):
x_old:=x_new:
y_old:=y_new:
od:
y_new:
end:

Thanks

## Solving ODEs without the Student package...

As it says in the title, I would like to solve the following ODE numerically using forward Euler method, without using the Student Package.

(dy(t))/(dt)=t(1-0.3t)-(ty)(1+0.6t)

with initial condition y(0)=1. I want to solve it for up to t=1, and then plot both the solution by Euler's method and the solution by "dsolve" on the same graph so I can compare them.

Also, can I make a separate DEplot with t extending to 5?

## Plot Interface and Euler Angles...

Can someone explain to me, if you can, how the Euler angles on the plot interface work?

It looks like Phi is the rotation around z, Theta is the rotation around x, and Psi is around y. I'm trying to use matrices to compute the vector that is pointing towards your face as you're looking at the plot with the given Euler angles.

X := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(phi), (2, 3) = sin(phi), (3, 1) = 0, (3, 2) = -sin(phi), (3, 3) = cos(phi)});

Y := Matrix(3, 3, {(1, 1) = cos(theta), (1, 2) = 0, (1, 3) = sin(theta), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(theta), (3, 2) = 0, (3, 3) = cos(theta)});

Z := Matrix(3, 3, {(1, 1) = cos(psi), (1, 2) = sin(psi), (1, 3) = 0, (2, 1) = -sin(psi), (2, 2) = cos(psi), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1});

and computing X*Y*Z*e3

TIA!

## Weird loop output limit, need assistance...

I am a student taking differential equations and I need to implement Euler's method using Maple 17. I have set up a do loop that looks like this:

`for i from 1 to n1 do`
`k:= f(t,v):`
`v:= v + h*k:`
`t := t + h:`
`od:`

Where n1 is initialized to 50, f(t,v) := 0.0207v2 -893.58, and h is 0.1. v and t are both initialized as 0.

## How to I create the Runge-Kutta's and Euler's meth...

Hi, I got a doubtI don’tknow how to make the Runge-Kutta’s and Euler’s method. The Runge-Kutta for thesecond and fourth order. I don’t know how to beginning the algoritms, I needsome help. Thanks.

## Recta de Euler

Maple

Aqui les dejo La ecuación de la Recta de Euler, calculado desde su inicio hasta la comprobación con el comando EulerLine.

Recta_de_Euler.mw

## could anyone help me with my euler plot too!...

[I split this off as a separate Question, cleaned up the machine-generated Title, added the Tags, and cleaned out some excessive blank lines.---Carl Love as Moderator]

could anyone help me with my euler plot too!

> with(plots):with(DEtools):

Equations & Initial conditions

> de1:=D(x)(t)=a*x(t)-q*x(t)*y(t)-n*x(t)*z(t);

>

## Integrating string of real Cos/Sine terms - gettin...

I am currently trying to integrate a long string of fractional sine and cos terms with a cos term on the denominator and other exponential multipliers, but all variables and coefficients are real (and I have put this assumption in Maple).

When I integrate them on Maple it is automatically simplifying the result using Euler's rule to give me a complex fraction with a complex numerator and denominator. This is not very helpful as I need to use the result in further calculation,...

## Help getting rid of a recursive assignment message...

`> with(plots);> u := proc (t, Q, dQdt) options operator, arrow; 0.15e-2*cos(omega*t...`