## ODE System Solve...

Asked by:

R2,R3,R4,R5 have been given,I try to solve the following ode equation: The initial value:r2(0)=r3(0)=r4(0)=r5#(0);system={diff(r2(theta),theta)=R2;diff(r3(theta),theta)=2*R2*U2+R3;diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4;diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5}.I want to get the exact solution of subs(theta=2*Pi,U5),But it just gives the form include _Z1,_Z_2,_Z3.How can I get exact value?

restart:

#interface(echo = 2)

 > c10:=-26/9:c01:=-9.330480048:c11:=-199/33:c02:=-7.162134941:c12:=-93/11:c03:=-.756797589:d10:=11/9:d01:=26/9:d11:=19/3:d02:=25/3:d12:=8:d03:=1:
 >
 >
A1 := c03*y^3+c12*x*y^2+c02*y^2+c11*x*y+c01*y+c10*x:B1:=d03*y^3+d12*x*y^2+d02*y^2+d11*x*y+d01*y+d10*x:
 > aa1:=diff(arctan(v/u),u):bb1:=diff(arctan(v/u),v):

A11:= subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, -A1):B11:= subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, B1):

 > w :=-c01*d10+c10*d01:
 > f11 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, -A1): collect(%, v):f2 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, B1): collect(%, v):g := simplify(-c10*f11/sqrt(w)+c01*f2/sqrt(w)): collect(%, v):
 > f111:=collect(1/sqrt(w)*f11,v):f222:=collect(1/sqrt(w)*g,v):
 > F1:=u*f111+v*f222:F11:=subs({u=r*cos(theta),v=r*sin(theta)},F1):F11:=F11/r:F2:=aa1*f111+bb1*f222:F22:=subs({u=r*cos(theta),v=r*sin(theta)},F2):
 > M:=F11/F22:M:=taylor(M,r,6):r1:=coeff(M,r,1):simplify(%):subs(c10=-d01,r1):simplify(%):
 >
 > c10:=-d01:R2:=coeff(M,r,2):R3:=coeff(M,r,3):R4:=coeff(M,r,4):R5:=coeff(M,r,5):
 >
 > #R2,R3,R4,R5 have been given,I try to solve the following ode equation: The initial value:r2(0)=r3(0)=r4(0)=r5#(0);system={diff(r2(theta),theta)=R2;diff(r3(theta),theta)=2*R2*U2+R3;diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4;diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5}.I want to get the exact solution of subs(theta=2*Pi,U5),But it just gives the form include _Z1,_Z_2,_Z3.How can I get exact value?
 >
 > U2:=rhs(dsolve({diff(r2(theta),theta)=R2,r2(0)=0})):
 > U3:=rhs(dsolve({diff(r3(theta),theta)=2*R2*U2+R3,r3(0)=0})):
 > U4:=rhs(dsolve({diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4,r4(0)=0})):
 > U5:=rhs(dsolve({diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5,r5(0)=0})):
 > U6:=subs(theta=2*Pi,U5):save U6, output5: ## drawing and calculation of an angle...

Asked by:

how to draw and calculate the angle of a dihedral of a regular tetrahedron ? Thank you.

## dimensionless dynamical system...

Asked by:

Hi everyone...

How can anyone help me in the attached file? I want to know how the equation of the system turned into a dimensionless

dynamical system?  ## Problem with `remove` command...

Asked by:

Dear friends, please I would like to ask for your help with an odd problem I have using the remove command.

I have an array

A:=Array([1,4,1,7]);

and I need to remove its first element A.

A:= remove[flatten](x -> x = A, A);

Instead of getting the result  A:= [4 1 7] I get  A:=[4 7], and I can't understand why.

Could you please help me with a solution to the problem? Many thanks for the help.

## SCI MODEL help with Equilibrium state and basic r...

Asked by:

Dear house

I am new to maple and will really appreciate some assistance in calculating the disease free , endemic equilibrium states and basic reproduction number for my model.

I have been trying for weeks. any asistance will be much appreciated

SCI_HELP.mw

## How do I find my unknown variable within a vector ...

Asked by:

Download Analisa_Dinamik_Limb_v1_(30).mwAnalisa_Dinamik_Limb_v1_(30).mw

So I have an equation that basically takes the component of vectors to be used as an equation. The variables that I after are FB1z, FB2x, and FB3y For example here is my equation:

EOM1:=(AFB1+AFB2+AFB3)=TEOM

EOM2:=(AFB1+AFB2+AFB3)=TEOM

EOM3:=(AFB1+AFB2+AFB3)-TEOM:

FBBp1:=FBPP1=(EulP1+EulP2+EulP3):
FBBp2:=FBPP2=(EulP1+EulP2+EulP3):
FBBp3:=FBPP3=(EulP1+EulP2+EulP3):

However there are unknown variable in AFB2 named FB2x and AFB3 named FB3y. Then AFB1 has unknown equation named FB1z and AFB3 has FB3y and so on. While in my FBBp1,FBBp2,and FBBp3 holds all of the variable of FB1z, FB2x, and FB3x
I have tried to use 'solve' command to find the variable but my computer won't stop processing it:
sls:=solve({EOM1,EOM2,EOM3,FBBp1,FBBp2,FBBp3},{FB1z,FB2x,FB3y}):

I tried to use the Gauss-Elimination by forming a matrix but it doesn't work as well since I am really confused how to take out the variables out of the vector component.

zzz:=Matrix([0,AFB2,AFB3,jjj],[AFB1,0,AFB3,jjj],[AFB1,AFB2,0,jjj],[FBP1,FBP2,FBP3,EulP],[FBP1,FBP2,FBP3,EulP],[FBP1,FBP2,FBP3,EulP]):
GaussElimination:=(zzz)

I would be very grateful If someone could help me. Thankyou

Edit: here are the .txt files and .mpl files that required to run the program

Inverse_Kinematics_ADRIAN2.mw

RotInertiax0_ADRIAN.txt

Download DisplacementXYZ.txt

inersia_platfrom.txt

There is an .mpl file that I couldn't upload so I will upload it in the comments

## Remember tables and forget command...

Asked by:

Dear friends, please I would like to ask for your help with the following problem:

I have a remember table generated by a recursive procedure

x:= proc(n)
option remember;
....
end proc:

It helps compute x(1), x(2), x(3), x(4).

After several additional steps I have a new x(2), say

x(2):= 3;

With this new x(2) I need to recompute x(3), x(4). I've tried

forget( x, [ x(3), x(4) ], subfunctions = false );

x(3);

x(4);

However, I do not get the new values of x(3) and x(4) but the old ones. What could it be wrong?

Many thanks for your help.

## Select element of rtable...

Asked by:

Dear friends,

I have to select the last element of a remember table T from a recursive procedure. I've tried

with(ListTools):

SelectLast(T);

as this command works with rtables, as it is stated in Maple's online help page. However I receive no result.

Can you please tell me how to obtain a correct result?

Many thanks for the help.

## How can I plot the solution curves for varying con...

Asked by:

Good day.

I have a simple function that I would like to plot, but am finding this awkward to do. My objective is to plot the function for varying k-values and I tried doing this using implicitplot and sequencing values of k.

The function in question is:
y := k*x*sqrt(z*(1-z));

The constant, k, takes the values: 5, 10, 15, ..., 100
The variables lie in the range: 0 ≤ x < 1 and 0 ≤ z < 1

So, if someone can tell me how to construct a plot of multiple solution curves for varying k, I would be most grateful.

Thanks for reading!

MaplePrimes_Plot.mw

## orthogonal affinity to oblique line and k ratio...

Asked by:

How to draw a circle transfomed by orthogonal affinity to oblique line and k ration ? Thank you.

## Spline Differentiation...

Asked by:

I have the numeric solution of differential equation and interpolate the data points with a spline of third degree. Is there a way of differentiating the spline as a whole? Differentiating every single polynom seems awkward.

## draw an ellipse in a rectangle...

Asked by:

How to draw an ellipse in a rectangle ? Thank you.

## how to find an ellipse inscribed in a given triang...

Asked by:

Is it  possible to draw an ellipse inscribled in a given triangle and we know its orthoptist circle ? Thank you very much.

## Find the focus of an ellipse with a tangential gen...

Asked by:
Etude d'un cas particulier a := 5: b := 7: k := 9: A := [a, 0]: B := [0, b]: #A et B fixes P := [t, 0]: Q := [0, k/t]:#P et Q 2 points mobiles cir := -a*x-b*y+x^2+y^2 = 0: sol := solve(subs(y = 5, cir), x): cen := [solve(diff(cir, x)), solve(diff(cir, y))]: x0 := sol: y0 := 5: M := [x0, y0]: R := sqrt(cen^2+cen^2): beta := arctan(diff(solve(EQ(M, cen), y), x)): Recherche des valeurs de t pour que les 2 droites soient perpendiculaires eq := t^2*(y0-b)+t*(a*b-a*y0+b*x0-k)-x0*(a*b-k) = 0; sol := solve(eq, t); t := sol; tp := sol; P1 := [t, 0]; Q1 := [0, k/t]; PQ1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0:#1ere tangente PQ2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0:#2ième tangente P2 := [tp, 0]; Q2 := [0, k/tp]; CIR := implicitplot(cir, x = -4 .. 8, y = -4 .. 12, color = red); Fig := proc (alpha) local Dr1, DR1, Dr2, DR2, N, u0, v0, Po, t, tp, sol; global a, b, k, cen, R; u0 := cen+R*cos(alpha); v0 := cen+R*sin(alpha); N := [u0, v0]; sol := solve(t^2*(v0-b)+t*(b*u0-a*v0+a*b-k)-u0*(a*b-k) = 0, t); t := sol; tp := sol; Dr1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0; DR1 := implicitplot(Dr1, x = -4 .. 8, y = -4 .. 12, color = brown); Dr2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0; DR2 := implicitplot(Dr2, x = -4 .. 8, y = -4 .. 12, color = pink); Po := pointplot([N[]], symbol = solidcircle, color = [black], symbolsize = 8); display([Po, DR1, DR2]) end proc; DrPQ1 := implicitplot(PQ1, x = -4 .. 22, y = -4 .. 12, color = blue); DrPQ2 := implicitplot(PQ2, x = -4 .. 22, y = -4 .. 12, color = blue); Points := pointplot([A[], B[], M[], P1[], P2[], Q1[], Q2[], cen[]], symbol = solidcircle, color = [green], symbolsize = 10); T := plots:-textplot([[A[], "A"], [B[], "B"], [M[], "M"], [P1[], "P1"], [P2[], "P2"], [Q1[], "Q1"], [Q2[], "Q2"], [cen[], "cen"]], font = [times, 10], align = {below, left}); n := 19; display([seq(Fig(2*i*Pi/n), i = 0 .. n), Fig(beta), CIR, DrPQ1, DrPQ2, Points, T], scaling = constrained, size = [500, 500]); I would find out the focus of the ellipse. Thank you.

## Don't know how to plot...

Asked by:

Please, anyone with the idea on how to plot D1 against alpha[n]. The link is attached below

Help!!!.mw

﻿