## 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

Some time ago, I have used the Virtual 3D Solar System code to plot a few interesting figures with asteroids. It can be found here: http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html . I plotted the asteroid belt as a closed, warped surface according to how the asteroids are inclined, with the arguments of perihelion and longitude of ascending node where they cross the equatorial plane to the other celestial hemisphere. The plot was only done with axes in units of distances, for convenience's sake in astronomical units of 1 AU = 150 million km.

But I am strongly wondering if it were somehow possible to alter or adjust the code such that there is a zylinder placed around such plot where one can see celestial coordinates (Rectascension, Declination) on the inside, so that if one wants to know what coordinates an orbit of a specific asteroid has that one can look in the chart and go out on the balcony and set the telescope to these coordinates. Of course the asteroid most likely is not there on his entire orbital path, but you have at least the location where the asteroid CAN be. Would this be possible to plot?

This probably doesn't work if a closed cylinder is placed around the Virtual Solar System. But how about scrolling the cylinder and the orbits flat on a 2D plot?

## 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.

## How to solve this equation?...

Hello!

If I type this into a CAS calculator from Texas, I get the right result for Uc wich is 545.2.

solve(Uc&angle;-90=400&angle;X-150&angle;0+j*174.4,Uc,X)

This is used in AC circuits.

However, in Maple I'm using polar coordinates, so Im using this preamble:

phasor := proc (r, theta) options operator, arrow; r*cos(convert(theta*degrees, radians))+I*r*sin(convert(theta*degrees, radians)) end proc

This basically means that I can write phasor(value,angle in degrees) and get the lenth and angle of a vector on the complex plane.

Basically I want to know how I can make Maple solve this:

evalf(solve({phasor(U__C, -90) = phasor(400, X)-phasor(150, 0)+phasor(174.4, 90)}, {Uc, X})) Where I'm just interested in U_C , X doesn't matter.

I can't figure out how to do this with my current preamble. Does anyone know how to make this work?

## 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.

## Setup custom indices in Physics + Bug?...

Hi,

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,

PhysicsBug.mw

## 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

## Plotting r = 1/cos(t) in polar coordinates...

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.