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I'm trying built a graph in cylindrical coordinates. I have 3 matrix X(20,30); Y(20,30), and temperatura T(20,30). The matrices X and Y are already in cylindrical coordinates. In matlab is just "pcolor (X,Y,T)". Anyone can help me?

X and Y are the coordinates of cylinder discretized (z was not included)

I have this plot in matlab, but i need it in maple.


Hello, I am working on an elektromagnetism assignment, and have hit a slight problem with the Physics[Vectors] package. The cartesian unit vectors are set to i, j and k. but at my school we have always used x, y and z for both the cartesian unit vectors and the cartesian coordinates. Is there a way to change this so that i am able to use _x, _y and _z istead?


P.S. This is my first post so sorry if it is badly done.



Is it possible convert some equations in R² (ellipse, hyperbola) to polar coordinates using Maple? And a regular  object in R³ like a sphere, a cylinder or a cube could be converted from cartesian coordinates to polar coordinates?


Thank you so much.


     I was wondering if there is an easy way to define another set of indices in the Physics package. For example, usually greek indices are for all 4 spacetime dimensions. Using Setup(spaceindices = lowercaselatin), we can define 3 of those as space indices. I was hoping there is a more general command, so that I could use only 2 indices as "space indices". For example, X[i] would run over x,y while X[mu] would run over t, z. Is there such a command in the Physics package, or a simple way to implement this personally?

Second thing. I was playing with SumOverRepeatedIndices on an expression that contained both space indices and spacetime indices. Usually this seems to work, but in my attached example it does not. I tried the same thing with just spacetime indices in Maple 18 (newest Physics update) and it gave the same error.

Any help appreciated,


Dear all
I am using Physics[Vectors] package of Maple 17. I want to define an orthogonal curvilinear coordinates through alpha and beta independent variables. To define unit vectors of alpha and beta, I have to apply the derivatives of position vector r_ with respect to alpha and beta, respectively. Please help me to define the unit vectors in directions alpha and beta as derivatives of position vector r_ with respect to alpha and beta, respectively. Please see the below Code:

> restart;

> with(Physics[Vectors]);

> Setup(mathematicalnotation=true);

> r_:=X(alpha,beta)*_i+Y(alpha,beta)*_j+Z(alpha,beta)*_k;

The unit vectors in directions alpha and beta should be defined as:


It is worthwhile to mention that the following expression governs:

> diff(r_,alpha).diff(r_,beta)=0;


Please guide me.

Best wishes


In the (r,t) polar coordinates, the graph of the equation r = 1/cos(t) should be a straight vertical line segment but Maple produces junk.  What is going on?

plot(1/cos(t), t=0..Pi/3, coords=polar);

The parametric version

plot([1/cos(t), t, t=0..Pi/3], coords=polar);

produces the same thing.

I am thinking about plotting a star chart of the whole sky. While it might not be difficult to get the (x,y)-coordinates of fairly good number of stars from star catalogues and to plot them accordingly in a 2d-plot, it might be more difficult to plot the stars according to their brightness. Also, I would like to plot the chart in cylindrical coordinate with astronomical coordinate axes for x and y. Moreover, only the brighter stars should be visible when the whole chart is shown, but when zooming in (while still having the axes visible) to have a closer look at some specific locations where I wand to make some square to show some fields, fainter stars should appear.

Is this possible in Maple ? I'd prefer to do a plot as I can really draw several squares where I want them which is not possible in my planetarium software.


I have modeled a slidercrank with absolute coordinates.

I have a slight problem when I want to mesure the Euler angles with Euler angle sensors.

In fact, the angle of the crank around the z axis (gamma1) always stay betwen -pi and pi. I would have like to see the value of my angle always increases with the evolution of the time since I impose a constant torque on the crank.

How can I do to observe the Euler angles of a body (parameterized with absolute coordinates) without any limit between [-pi,pi]?

Thank you for your help.

PS: I insert my model attached


Hello every one.

I want to do some tensor computations in maple in a specified coordinate system but I don't know how! As an example I ask the follwing question.

Consider a second order symmetric tensor "A". I want to compute the components of "curl(curl(A))" in cylinderical coordinates. How should I do this in maple?

This is related to a famous equation in elasticity known as "small strain compatibility" equation.

Thanks for the help

In Maple15, in spherical coordinates, what statements plot covariant vector [1,r^2*sin(theta),sin^2(theta)] and its contravariant equivalent [1,sin(theta),1/r^2] within their respective bases vectors. Assume r = 2, theta = pi/6 and phi = pi/4. I presume each plot will display the same space vector.

The Maple help definition for spherical coordinates uses the triple (r, φ, θ) (Note the ordering!!) with φ in the range 0..Π and θ in the range 0..2Π. This means that the second entry in the triple is the zenith angle (latitude) and the third entry in th triple is the azimuth angle (longitude). This is confirmed by the relation to cartesian coordinates stated on the definition page as
x= r sin(φ) cos(θ)

y= r sin(φ) sin(θ)

z= r cos(φ)

However the help page for coords has spherical polars defined by the triple (u, v, w), with the relation to cartesian coordinates given as

x= u cos(v) sin(w)

y= u sin(v) sin(w)

z= u cos(w)

which suggests that this time it is the third entry in the triple (ie w) which is the zenith angle (latitude), with the second entry being the azimuth (longitude).

My simple-minded attempt to check which of these interpretations is correct is shown in the attached worksheet. This seems to confirm that the MapleHelp definitions page is correct and the help/coords page is incorrect - or am I missing something??




Hi all,


I'm trying to initialize a 4-vector and promote it as a tensor in Maple 16 using the Physics package. My attempt so far has been unsuccessful :) 

This 4-vector needs to be a function of the coordinates X. What I'm trying to do is to allocate terms by terms my tensor as indicated in my attempt below. Everything looks fine (the query is telling me F2 is a tensor) but when I'm trying to compute contravariant quantities, I can't obtain an answer for a given coordinate (here F2[~n](X) is not equal du v_1(X))... Finally, the last line, computing the sum over all the indexes is not giving me an answer... 


restart; with(Physics):
Setup(coordinatesystems = cartesian):








Surely, something is wrong in my way of defining a spacetime tensor. What would be the solution to obtain a decent contravariant F2?


Another more or less related question would be to know how to compute a taylor expansion of a function itself i.e. 1/(1+f(X))~ 1-f(X) since f<<1? Would there be a built-in fonction to do such a thing?


Many thanks!




I have been trying to compute the analytical solution of two dimensional diffusion equation with zero neumann boundary conditions (no-flux) in polar coordinates using the solution in Andrei Polyanin's book. When I use 2d Gaussian function as initial condition, i cannot get the result. If I use some nicer function like f(r,phi)=1-r; there is no problem.  

Any idea why this happens? or any suggestion to compute the analytical solution?



M := Matrix([[3.83170597020751, 7.01558666981561, 10.1734681350627, 13.3236919363142, 16.4706300508776], [1.84118378134065, 5.33144277352503, 8.53631636634628, 11.7060049025920, 14.8635886339090], [3.05423692822714, 6.70613319415845, 9.96946782308759, 13.1703708560161, 16.3475223183217], [4.20118894121052, 8.01523659837595, 11.3459243107430, 14.5858482861670, 17.7887478660664], [5.31755312608399, 9.28239628524161, 12.6819084426388, 15.9641070377315, 19.1960288000489], [6.41561637570024, 10.5198608737723, 13.9871886301403, 17.3128424878846, 20.5755145213868], [7.50126614468414, 11.7349359530427, 15.2681814610978, 18.6374430096662, 21.9317150178022], [8.57783648971407, 12.9323862370895, 16.5293658843669, 19.9418533665273, 23.2680529264575], [9.64742165199721, 14.1155189078946, 17.7740123669152, 21.2290626228531, 24.5871974863176], [10.7114339706999, 15.2867376673329, 19.0045935379460, 22.5013987267772, 25.8912772768391], [11.7708766749555, 16.4478527484865, 20.2230314126817, 23.7607158603274, 27.1820215271905]]):

c := 10:

A := 5:

w := proc (r, phi, t) options operator, arrow; int(int(f(xi, eta)*G(r, phi, xi, eta, t)*xi, xi = 0 .. 5), eta = 0 .. 2*Pi) end proc:


Warning,  computation interrupted





I need to build a multibody model in MapleSim 6.4 in which with few global parameters I can describe all the other parameters. In other words the final user will enter this few parameters, that are coordinates of specific points, and then the model will calculate all the relative distances on the base of those coordinates.

The problem is that if I apply trigonometric function and square root (like in the screenshot) the model is not calculating any value. Is it possible to make those calculculations?


this is the model (don't worry about the nonsense plots, it's because it's not ultimated):






Let Poly2 denote the vector space of polynomials

(with real coefficients) of degree less than 3.

Poly2 = {a1t^2+ a2 t+ a3 |a1; a2; a3 €R}

You may assume that {1,t; t^2}is a basis for Poly2.

(1) Show that L1 = {t^2 + 1; t-2 ; t + 3}and L2 = {2 t^2 + t; t^2 + 3; t}

are bases for Poly2.

(2) Let v = 8t^2- 4t + 6 and w = 7t^2- t + 9. Find the coordinates for

v and w with respect to the basis L1 and with respect to the basis L2

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