## metric and coordinate change...

Hi,

I want to know is maple helpful to find a cjange coordinate to transform an old coordinate to a new coordinate? details are attached to the file:

changecoor.mw

Thanks guyz

## Change coords, from cylindrical or spherical to ca...

Hello.

If I have several equation where some of them are given in cartesian and some in spherical I would want to work with all surfaces in cartesian coordinates. Just since that is the coordinate system i´m most familiar with.

I have cheked and tried: ChangeOfVariables, changecoords and ?coords

All of those are great recourses, but they wont let me change from [r,theta,phi],cartesian[x,y,z] How can I obtain that in maple?

## Possible to work with Riemann Normal Coordinates i...

I would like work in Riemann Normal Coordinates, and derive expansion in number of derivatives of the metric.

For example, starting with the expansion of the metric in Riemann Normal Coordinates (assuming this needs not be derived)

$\displaystyle \begin{array}{rcl} g_{ij}(x)&=& \delta_{ij} -\frac 1 3 R_{iklj}x^kx^l -\frac 1 6 R_{iklj;m} x^kx^lx^m\\ &&+ (\frac2{45} R_{ilmk}R_{jpqk}- \frac 1 {20} R_{ilmj;pq})x^lx^m x^p x^q\\ &&+(-\frac 1{90} R_{iklj;mpq}+\frac 2{45} R_{iklr;m}R_{jpqr})x^kx^lx^mx^px^q\\ && +(-\frac 1 {504}R_{iklj;mpqr}+ \frac{17}{1260}R_{ikls;pq}R_{jmps}+ \frac{11}{1008}R_{ikls;q}R_{jmps;r}\\ && +\frac 1{315}R_{ilms}R_{jqrt}R_{kspt})x^kx^lx^mx^px^qx^r +O(|x|^7). \end{array}$

I would like to express the lapliacian, or square-root of the determinant ... etc., in terms of this metric and derive an expansion for them.

However, I cannot even define the metric as such in Maple-Physics, because the coefficients of xk depend themselfs upon the metric to be defined.

Is there a way to do such calculations in Maple ?

## Points on the coordinate plane

by: Maple

Points on the coordinate plane

(Guidance manual for the 6th class)

Changing the initial coordinates and going through the entire program first, we get a new picture-task

And Another     Coordinate_plane.mws

## Plot a path knowing x and y in function of a varia...

I need to plot a path with curvilinear coordinates. Knowing the curvature theta and length s of  parts that compose it, I found the equations of x and y as a function of the parameter s that goes from zero to the total length.
I make an example below:

for 0 <s <2,     x = s     and

y = 0 (straight line)

for 2 <s <2 + Pi,        x = 2 + 2 * sin ((s-2) / 2)      and

y = 2 * (1-cos ((s-2) / 2)

Now I want to find the corresponding plot of x (s), y (s) (without showing s as coordinate) but I do not know what commands I can use. Can you suggest me something? Thank you

## Find all coordinates of the graph...

I have plotted an equation which is in terms of 'a & omega'

Now i need coordinates of every points as an n*2 matrix

 (1)

## Higher order derivatives...

Consider, say, the following third order derivative:

expr := diff(f(x,y),x,y\$2);

Does there in Maple exist some built-in functions for extracting from such an expression 1.) the function being differentiated, and 2.) the coordinates being differentiated with respect to? Using op(expr) is of no immediate avail as it returns only a second order derivative (as the first operand), and one of the coordinates being differentiated with respect to (as the second operand).

It is, of course, possible to make ones own function for extracting these two quantities, a crude example being

splitDeriv := proc(expr,coords::expects(list) := [])   if PDETools:-difforder(expr) > 0 then      splitDeriv(op(1,expr),[coords[],op(2,expr)])   else      expr,coords   end ifend proc:

for which

splitDeriv(expr);

But it would be much nicer to use built-in functions. And perhaps such functions do exist. If so, I am unable to locate them. Perhaps I am just being stupid, for the problem seems rather elementary.

## The equivalent of pcolor from matlab in maple...

Hello,

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.

Thanks

## Cartesian unit vectors...

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.

## Converting cartesian to polar coordinates...

Hello!

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.

## How to define unit vectors of curvilinear coordina...

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:

_alpha=diff(r_,alpha)
_beta=diff(r_,beta)

It is worthwhile to mention that the following expression governs:

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

Best wishes

Ali

## How to create a zoomable star chart...

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.

## Tensor Computations in Maple...

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

## How do I plot co- and contra-variant spherical vec...

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.

## Defining a 4-vector in Maple 16...

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(mathematicalnotation=true):
Setup(coordinatesystems = cartesian):
Define();
g_[]:

F2[1]:=(x,y,z,t)->v_1(X);F2[2]:=(x,y,z,t)->v_2(X);F2[3]:=(x,y,z,t)->v_3(X);F2[4]:=(x,y,z,t)->1;

Define(F2[mu](X));

Define(F2,query);

F2[1](X);F2[2](X);

F2[~1](X);F2[~2](X);

F2[~nu].F2[nu]

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!

Vincent

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