I have a problem calculating integral analytically.

Can anyone help me in this regard?

Thanks

problem_2_integral_&_moshtagh.mw

Dear Maple experts,

is there a possibility/command to get a vizualization of the output of the command FeedbackConnect?

I was thinking of something like this:


as it is given on the maple-help page for that command (but not generated via a maple command as far as I understood)

Thanks in advance !

Dear Maple experts,

I try to avoid the generation of new variable names (for states, inputs, outputs) introduced automatically by maple (StateSpace(), FeedbackConnect()) in the two (connected) cases:

1)

I generated a discrete StateSpace system using a difference equation:

sys2 := StateSpace([u(n)=K_virt*(q_a(n)-q_d)+D_virt*(q_a(n)-q_a(n-1))/T],inputvariable=[q_a(n)],outputvariable=[u(n)],discrete=true,sampletime=T);

The statevariable "x1(n)" is automatically generated by maple

I tried to avoid this by using the following commands that don't work:

sys2 := StateSpace([u(n)=K_virt*(q_a(n)-q_d)+D_virt*(q_a(n)-q_a(n-1))/T],inputvariable=[q_a(n)],outputvariable=[u(n)],statevariable=[q_a(n-1)],discrete=true,sampletime=T);

-> error message:

Error, (in ProcessOptions) argument 'statevariable = [q_a(n-1)]' invalid: rhs should be of type list({name, anyfunc(name)})

sys2 := StateSpace([u(n)=K_virt*(q_a(n)-q_d)+D_virt*(q_a(n)-q_a(n-1))/T],inputvariable=[q_a(n)],outputvariable=[u(n)],statevariable=[q_a_delayed],discrete=true,sampletime=T);

-> error message:

Error, (in DynamicSystems:-StateSpace) missing state(s): {q_a_delayed(n)}

sys2 := StateSpace([u(n)=K_virt*(q_a(n)-q_d)+D_virt*(q_a(n)-q_a(n-1))/T],inputvariable=[q_a(n)],outputvariable=[u(n)],statevariable=[q_a_delayed(n)],discrete=true,sampletime=T);

-> error message:

Error, (in DynamicSystems:-StateSpace) missing state(s): {q_a_delayed(n)}

Can you help me here?

2)

I have two discrete StateSpace models (sys1, sys2):

* sys2 is the one from above (1 input, 1 output, 1 state)

* sys1 (2 inputs, 4 outputs, 4 states) doesn't contain any automatically generated variables (I obtained this one by transforming a continuous statespace model to a discrete one)

* variables that represent the same signal have the same name in both systems.

   -> "q_a(n)" appears as an output in sys1 and as an input in in sys2

   -> "u(n)"     appears as an input in sys1 and as an output in in sys2

Now I combined these two models via:

FeedbackConnect([sys1, sys2],[[2,2,1,-1]])

Instead of using the variable names I introduced maple generates new variable names for inputs, outputs and states.

How can I avoid this?

(the option "merge=evaluate") seems not to work (even if I work with numeric values for the system parameters instead of symbols)

Thank you in advance!

I ran the Fourier Transform about 6 months ago.

>

>

The out put was 23 lines long, and then used the Simplify/Simplify option for the result to obtain

, a relatively easier result.

I tried to re-run it today but it just gave me

with the result

Do you have any idea as to why this happens?? I seem to recall there may be similar “memory” problem

that occurred in the past.

Hello,

I tried to apply Berlekamp's theory to the polynomial X^9+X^6-X+1 in F3.
The matrix of the linear application whose kernel dimension is sought is:

 The dimension should be equal to 2 according to the theory since this polynomial decomposes into 2 irreducible polynomials.
However, the nullspace instruction of maple does not give a result consistent with the theory. Please help me find what is happening.

Hello
Can you tell me how to use rank and nullspace instructions in linear algebra with maple 2023.
Here is a preview of my work that produces nothing?
Thanks

I have constructed two Random Variables (X1 and X2).  They work the way I want.  When I take the abs(X1-X2) and ask for the PDF, I get output with Elliptic functions that seems to be in complex space. I read about the Elliptic functions, but got nowhere -- above my head.

I only want the "real" output on the 0 <= t <= 2 domain.  Does anyone know how to parse this output so that I can see a PDF as a function of t?

Download AbsDiff.mw

Hi! I have a problem that is driving me crazy. It is related to shooting methods for ODEs with Maple. Essentially what one needs is to find the solution to two equations simultaneously, defined in terms of the numerical solution to a second-order differential equation. I have used fsolve and also DirectSearch but nothing works. Graphically one can see the solution to the problem exists.

I include the Maple file. Thank you. 

Download shooting_question.mw

I am in the process of trying to learn Maple. As an exercise I am trying to plot an amplitude modulated waveform. No problem plotting the waveform of the carrier and the modulating signal but for some reason (user error on my part) I can't plot the combined waveform y given by. 

y = [1 + M*cos(2*Pi*f__m*t)]*A*sin(2*Pi*f__c*t)

Where the following values have been set M = 0.5, A = 1, f_m = 2, f_c = 10.

Plotting y using the following

plot(y, t = 0 .. 1, title = "Graph of Carrier", labels = ["time (seconds)", "Amplitude (Volts)"], color = red);

Gives the following error. Having tried various combinations of variables, values, single parameter functions etc I need a pointer as to where I am going wrong. 

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
What I am expecting is a graph similar to the below derived in Excel? My version of Maple is 2023.2

I have plotted a 3D figure by maple 2023. but all numbers and units on axes are seen a black boxes. How can fix this problem?

After my maple (2023) had a crash (froze) and i forc closed it all my files are opened and then changed. All equation fields are changed into "Maple Input" type equations. This completely ruins all my "document" type files where the appearance of the equations was important. More than that most of the changed equations give rise to errors. So the file is basically destroyed. The odd thing is that the file looks fine the first few seconds, but then it is changed completely.
I have uninstalled 2023, and installed Maple 2024 without success. 

Plz help!

How do I get Maple 2023 to simplify/combine units in results?  For example,

Quantity(3.3897859*Unit(km^2)/Unit(m^2), 0.2) ;

should simplify to

Quantity(3389785.9, 0.2) ;

The full example where the problem occurs is given below.

alias(l = log10, l100 = log[100], pi[0] = Pi, r = sqrt, S_ellipsoid = ellipsoid) :
with(ScientificErrorAnalysis) :
with(Units) :

_km := Unit(km) :
_lm := Unit(lm) :
_lx := Unit(lx) :
_m := Unit(m) :
_rev := Unit(rev) :
alias(Q = Quantity) :
AddUnit(astronomical_unit, context = astronomy, default = true, conversion = 149597870700*m) :
pi := pi[0] :
S_spheroid := (a, b) -> S_ellipsoid(a, a, b) :

_AU := Unit(AU) :
a_Mars := Q(227939366., 1.)*_km : ##
a_Terra := Q(149598023., 1.)*_km : ##
alpha_Phobos := Q(9517.58, 0.01)*_km : ##
B_Phobos := Q(0.071, 0.012) :
d_x_Phobos := Q(25.90, 0.08)*_km :
d_y_Phobos := Q(22.60, 0.08)*_km :
d_z_Phobos := Q(18.32, 0.06)*_km :
E_I := _lx :
H_Mars := -Q(1.5, 0.1) : ##
L_Sol := Q(3.75E28, 0.01E28)*_lm : ##
m_E := -Q(14.18, 0.01) : ##
pi_Phobos := Q(9234.42, 0.01)*_km : ##
r_e_Mars := Q(3396.2, 0.1)*_km :
r_e_Terra := Q(6378137.0, 0.1)*_m : ##
S_sphere := r -> S_spheroid(r, r) :
theta_rev := _rev :

a_Phobos := (alpha_Phobos + pi_Phobos)/2 :
Delta_Sol := a_Terra - r_e_Terra : 
l_A := _AU :
m := E -> m_E - 5*l100(E/E_I) :
r_x_Phobos := d_x_Phobos/2 :
r_y_Phobos := d_y_Phobos/2 :
r_z_Phobos := d_z_Phobos/2 :
theta_rev2 := theta_rev/2 :

Delta_Mars := r(a_Mars^2 + Delta_Sol^2) : 
q := theta -> 2*((sin(theta)/pi) + (1 - (theta/theta_rev2))*cos(theta))/3 :
r_e_Phobos := (r_x_Phobos + r_y_Phobos)/2 :
S_Phobos := S_ellipsoid(r_x_Phobos, r_y_Phobos, r_z_Phobos) :

Delta_Phobos := Delta_Mars : 
L_Phobos := B_Phobos*L_Sol*S_Phobos/(2*S_sphere(a_Mars)) :
mu_Mars := 5*l(a_Mars*Delta_Mars/l_A^2) : 
rho_e_Mars := arcsin(r_e_Mars/Delta_Mars) :
theta_Mars := arccos((a_Mars^2 + Delta_Mars^2 - Delta_Sol^2)/(2*a_Mars*Delta_Mars)) :

E_Phobos := L_Phobos/S_sphere(Delta_Phobos) :
m_Mars := H_Mars + mu_Mars - 5*l100(q(theta_Mars)) :
rho_e_Phobos := arcsin(r_e_Phobos/Delta_Phobos) :
rho_o_Phobos := arctan(a_Phobos/Delta_Phobos) :

Deltarho_Phobos := rho_o_Phobos - rho_e_Mars - rho_e_Phobos :
m_Phobos := m(E_Phobos) :

Deltam_Phobos := m_Phobos - m_Mars :

Deltarhostar_Phobos := Deltarho_Phobos/Deltam_Phobos :

"Phobos apparent logarithmic brightness in astronomical magnitudes" = combine(m_Phobos, errors) ;
"Mars-Phobos apparent angular separation in arcseconds" = combine(convert(Deltarhostar_Phobos, units, arcsec), errors) ;

(*
https://www.nicolesharp.net/wiki/Solar_System_data_for_Maple
https://en.wikipedia.org/wiki/astronomical_unit
https://en.wikipedia.org/wiki/Star_Sol
https://en.wikipedia.org/wiki/Planet_Terra
https://en.wikipedia.org/wiki/Terran_radius
https://en.wikipedia.org/wiki/WGS84
https://en.wikipedia.org/wiki/Planet_Mars
https://en.wikipedia.org/wiki/Satellite_Phobos
https://en.wikipedia.org/wiki/Solar_System_by_size
https://en.wikipedia.org/wiki/illuminance
*)

Hi,

Experiencing the following problem.  One of our servers was cloned, the GUID was replaced and then rejoined to the domain.  All applications are working exept Maple.  The application launches but then closes right away.  No error messages provided so not sure where else to look for possible fixes to this problem.  The application is runing on Server 2022.

Thank you.

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.

Can someone tell me how to calculate the Christoffel symbols in spherical coordinates in Euclidean three dimensional space?

Thank you very much in advance!