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i will solve the three equations below with numerical method,how?

eq1 := -2.517407096*10^12*q[1](t)^2-5.292771429*10^12*q[1](t)-1.888055322*10^12*q[2](t) = 0
eq2 := 2.246321962*10^12*q[1](t)^2+1.684741471*10^12*q[2](t)+8.110113889*10^12*q[1](t)-7.480938859*10^10*q[3](t) = 0
eq3 := int((-3.826000000*10^11*q[2](t)*cos(Pi*x)*Pi^2-3.826000000*10^11*q[1](t)^2*cos(Pi*x)*Pi^3*sin(Pi*x)+3.414000000*10^11*q[1](t)^2*sin(Pi*x)^2*Pi^4-3.414000000*10^11*q[1](t)^2*cos(Pi*x)^2*Pi^4+7*(int(exp(10*tau), tau = -infinity .. t))+q(x, t))*sin(Pi*x), x = 0 .. 1) = 0

Hello everybody,

I'm trying to solve for a challenging problem : a moving inclined plane with a block

I want to solve for the acceleration components for the block and the plane and the normal force acting on the block.

Let O=(0,0) be an external origin.

Let h be the upper left height of the inclined plane.

Let x1 be the x-position of the center of gravity of the inclined plane.

Let x2 be the x-postion of the center of gravity of the block.

Let y be the y-position of the center of gravity of the block.

Let m1 be the mass of the plane. Let m2 be the mass of the block.

Let  mu[1] be the coeffiction of kinetic friction between the bottom of the inclined plane and the level surface.

Let mu[2]  be the coeffiction of kinetic friction between the block and the upper surface of the inclined plane.

Let theta be the angle of the plane with the horizontal.

Let Fp a force applied to the inclined plane.


With those defined variables, I make two separable free body diagrams for the block and for the inclined plane, indicating all of the external forces acting on each. It then comes those two vectorial equations :

Block : m2a2=Wweight of block+Fplan acting on block+Ffriction from plan to block+Nnormal from plan to block

Plane : m1a1=Wweight of plane+Fpushing force+Fblock acting on plane+Ffriction from level to plan+Nnormal from level to plane+Ffriction from block to plane+Nnormal from block to plane

I am quite not sure whether I should include the Ffriction from block to plane and the Nnormal from block to plane into the plane's acceleration calculation. Am I right ?

I notice that from the geometry of the figure, I can write down the relation : tan(theta)=(h-y)/(x2-x1)

This implies the relation : -a2y=tan(theta)(a2x-a1x) (equation 1)

Writing down the equations for the x- and y- components of the accelerations of the block and of the plane , this yields :

( equation 2) : m2a2x=m1 sqrt(a1x2+a1y2) cos(theta) -    mu[2]  N1 sin(theta) +Ncos(theta


(equation 3) : m2a2y= m2g+m1 sqrt(a1x2+a1y2) sin(theta) +  mu[2]  N1 cos(theta) +Nsin(theta

(equation 4) : m1a1x=Fp - m2 sqrt(a2x2+a2y2)  sin(theta) +  mu[2]  N1 cos(theta) - Ncos(theta

(equation 5) : m1a1y=-m1g  - m2 sqrt(a2x2+a2y2)  cos(theta) - mu[1] N1 + N1 -  mu[2]  N1 sin(theta) -  mu[2]  N1 cos(theta)

Since N1=m1g,  equation 5 becomes : m1a1y= - m2 sqrt(a2x2+a2y2)  cos(theta)   -  mu[2]  N1 sin(theta) -  mu[2]  N1 cos(theta)

I am confused at this stage because a1y=0, that is to say, the plane remains at the ground level surface.

Where am I wrong ? Does this comes from my previous question ?


I want to solve this problem with Maple and plot the solutions. Thank you for any answer !



I could obtain the simulation of my multibody with kinematic closed chain (CKC).

However, it seems that from a specific time (around 12s) in my model I believe that I have some numerical instabilities. Indeed, I could compare my simulation results with another mulbody software. I obtain the same simulation until 12s and after in MapleSim, it appears many perturbations as you can see on the figures belows.

So, I think that I tune the numerical solver. This numerical solver must solve DAEs equations since my model contains 4 kinematic closed loops.

If i read correctly the help menu, there are the following methods to solve the DAEs :

- use specific DAE numerical solver (3 differents solvers are used : ck45 method, RKF45 method and Rosenbrock method

- use reformulation equations techniques (Baumgarte, Projection) which can be associated (I believe) with a classic solver like (RK4).

For the moment, I have obtained my results with the rosenbrock solver with error absolute : 1.0*10^(-4) and eror relative :error absolute : 1.0*10^(-4) 

Do you have some ideas or advices so as to find a better method to solve my multibody systems with kinematic closed loops ? This method should  prevent the creation of numerical instabilities.

Thanks a lot for your help


Hi Everyone

Is there a built-in way to fit a regression using generalized least squares in Maple ?



I would like to apply a torque directly on a revolute joint. I use a torque modulated by a signal source which is modified chirp signal.

I have done like in the figure below :

After having added this torque, my model no longer runs. The error message is only "simulation interrupted".

Do I correctly plug the torque ? Should I plug the torque element more in the flange a or b of the considered revolute joint ?

Do I tick "use support flange" ? Anyway, with or without, my model crashes.

Thanks a lot for your help.




I am using densityplot function to produce different plots of a function. The function depends on two variables q and yi .

densityplot(f, q = 0 .. 1, yi = 0 .. 1, grid = [100, 100], style = patchnogrid, color = "Red", axes = boxed, axesfont = [Times, Roman, 15], labelfont = [Times, Roman, 15])

I pass the command style = patchnogrid, but still I get these white lines which I believe are grid lines. 
In the example provided in maple tutorial, when they used this command, all gridlines were removed. Why are they not removed in my plots?

if the plot is not visible, click the link


I have used the command "op" in a code that I have written with Maple 17. When I restart the maple server and run the whole code again, the result of the "op" command changes! why is this happening?

Hi all

How can I produce following matrix by maple?

the order of matrix should be {N*(m+1)}*{N*(m+1)} where N is known constant


thanks for any guide


Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

How do you use algcurves and Puiseux series in Maple?

Simplify matrix...

August 28 2014 Leon 0

Dear all,


I've a very complicated matrix, and I'm unable to read the result by maple. It should be a 6x6 matrix.

What mean the following expression ?

Thank you for your help.





I trying to simulate a force sensor on robot arm, but every time I try something, I get nothing from my sensor, can you help me?


Here it's my "design":


Also, if I add a rigid body I get this error:





I am trying to plot only the real part of the values obtained from the MapleSim model.  Probably there is a Modelica function to get only the real part of the values, but I am unable to find it. Could you please have a look at the code and let me know what I should do to solve this problem?




The code is: (I want to plot the real part of R2)


model IKTest

parameter Boolean switched = false;
parameter Modelica.SIunits.Length L1 = 0.100;
parameter Modelica.SIunits.Length L2 = 0.102;
parameter Modelica.SIunits.Length L3 = 0.5;
//parameter Real c; //Complex number
//parameter c;

Modelica.Blocks.Interfaces.RealInput u[3]
annotation (Placement(transformation(extent={{-140,-20},{-100,20}},rotation=0)));
Modelica.Blocks.Interfaces.RealOutput y[3]
annotation (Placement(transformation(extent={{90,-10},{110,10}},rotation=0)));

Real Tx = u[1];
Real Ty = u[2];
Real Tz = u[3];
Real R1 = y[1];
Real R2 = y[2];
Real R3 = y[3];




annotation (uses(Modelica(version = "3.1")));
end IKTest;

Phil Yasskin (Texas A&M) has prepared a maplet for the Maplets for Calculus proiect. While this maplet works, in Malmem 18 it sometimes does NOT display the plot. We don't see this behavior in Maple 17, The maplet is attached for your convenience, if you are interested in seeing if it works for you.

The problem is difficult to describe. Basically, at the end of the problem, users can elect to see a plot of the function with(some) asymptotes. The code creates the plot when the problem is created, and displays this plot in the worksheet. But, when the plot is requested within the mapmlet, it sometimes does not show in the empty plot window.

Any explanations (or followup quesitons) will be greatly appreciated.


Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail:
Phone:  (803) 777-6183         URL:


I read this thread, but it didnt really help. (i noticed an error in the expression pj, now fixed!)

See this file above.

The function needs to be maximized is "loglik", with constraints,

f0>0, sigma>0 and mu is FREE. Only three variables.


Using some calculus and by changing variables, I was able to use Gauss–Hermite quadrature, and do some approximation, to get the values:





I am wondering if Maple can do this straight away. By that, I mean, without doing much further,  how could I get the values? (most efficiently and quickly)





Hi Again

Assume that we have known matrix namely, Q, of order (m+1)*(m+1) and we want to construct following matrix

where 0(bar) is zero matrix of orde (m+1)*(m+1) and New matrix should be of order {N*(m+1)}*{N*(m+1)} where N is known constant.

thanks for any guide

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

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