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):
> 
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:


Download Li2.mw
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[1].
A:= remove[flatten](x > x = A[1], 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.
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[1]+AFB2[1]+AFB3[1])=TEOM[1]
EOM2:=(AFB1[2]+AFB2[2]+AFB3[2])=TEOM[2]
EOM3:=(AFB1[3]+AFB2[3]+AFB3[3])TEOM[3]:
FBBp1:=FBPP1=(EulP1[1]+EulP2[1]+EulP3[1]):
FBBp2:=FBPP2=(EulP1[2]+EulP2[2]+EulP3[2]):
FBBp3:=FBPP3=(EulP1[3]+EulP2[3]+EulP3[3]):
However there are unknown variable in AFB2[1] named FB2x and AFB3[1] named FB3y. Then AFB1[2] has unknown equation named FB1z and AFB3[2] 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 GaussElimination 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[1],AFB3[1],jjj[1]],[AFB1[2],0,AFB3[2],jjj[2]],[AFB1[3],AFB2[3],0,jjj[3]],[FBP1[1],FBP2[1],FBP3[1],EulP[1]],[FBP1[2],FBP2[2],FBP3[2],EulP[2]],[FBP1[3],FBP2[3],FBP3[3],EulP[3]]):
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
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.
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.
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 kvalues and I tried doing this using implicitplot and sequencing values of k.
The function in question is:
y := k*x*sqrt(z*(1z));
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
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.
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*xb*y+x^2+y^2 = 0:
sol := solve(subs(y = 5, cir), x):
cen := [solve(diff(cir, x)), solve(diff(cir, y))]:
x0 := sol[1]: y0 := 5:
M := [x0, y0]:
R := sqrt(cen[1]^2+cen[2]^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*(y0b)+t*(a*ba*y0+b*x0k)x0*(a*bk) = 0;
sol := solve(eq, t);
t := sol[1]; tp := sol[2];
P1 := [t, 0]; Q1 := [0, k/t];
PQ1 := simplify(x*(a*b+b*t+k)+y*t*(ta)t*(a*b+b*t+k)) = 0:#1ere tangente
PQ2 := simplify(x*(a*b+b*tp+k)+y*tp*(tpa)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[1]+R*cos(alpha); v0 := cen[2]+R*sin(alpha); N := [u0, v0]; sol := solve(t^2*(v0b)+t*(b*u0a*v0+a*bk)u0*(a*bk) = 0, t); t := sol[1]; tp := sol[2]; Dr1 := simplify(x*(a*b+b*t+k)+y*t*(ta)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*(tpa)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.