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## Name

potrot - query a NEMO potential in the XY plane, and derive a rotation curve

## Synopsis

potrot [parameter=value]

## Description

potrot computed the "rotation curve" (as defined by sqrt(radius*radial_force)) of a potential. Single slit rotation curves can be defined (by using a single given angle p=) as well as averaged along a set of position angles (e.g. p=0:90:2).

## Parameters

The following parameters are recognized in any order if the keyword is also given:
potname=
Name of potential, no default.
potpars=
Parameters for potential (1st one is pattern speed). See potential(5NEMO) for some examples.
potfile=
Any optional data file associated with potential.
r=
Radii to sample. Notice for most potentials r=0 results in NaN’s or divisions by zero and generally bad output. [0:2:0.1]
p=
Angles to sample (in degrees). If exactly two angles are given, and niter > 0, an iterative approach is used (similar to the one in potq(1NEMO) ) and is generally more accurate. If One angle is given, an exact "rotation curve" along that (position) angle is give, else an average force is used to derive the "rotation curve". Default: 0. (meaning slit rotation curve along the X axis)
t=
Time to test potential at, if relevant [0.0]
omega=
Use this instead of any returned pattern speed.
format=
Format used to print numbers [%g] **not used yet**
niter=
Maximum number of iterations to find the forces from which the rotation curve is derived. Only used if exactly two angles p are given. Careful: at each iteration the sample step is halved, doubling the CPU requirements. 
eps=
Relative accuracy that stops the iterations. [0.001]

## Examples

Here is an example of taking a "rotation curve" along the major, minor and force average of a Pfenniger(1984) bar. The three tables are then cut into a simpler form and plotted using tabplot. With the default pgplot interface for yapp they are colored rsp. red, green and blue.
```potrot pfenniger84 r=0.1:10:0.1 p=0      > tab1
potrot pfenniger84 r=0.1:10:0.1 p=90     > tab2
potrot pfenniger84 r=0.1:10:0.1 p=0:90:2 > tab3
tabmath tab1,tab2,tab3 - %1,%3,%6,%9 all | tabplot - 1 2,3,4 line=1,1 color=2,3,4
```
Here’s a comparison between various methods for the same Pfenniger potential, at a radius where the force along major and minor axis differs most:
```potrot pfenniger84 r=4 p=0
4 -0.0403306 0.401649
potrot pfenniger84 r=4 p=90
4 -0.0277544 0.333193
potrot pfenniger84 r=4 p=0:90:10
4 -0.031413 0.354474
potrot pfenniger84 r=4 p=0:90:2
4 -0.0311816 0.353166
potrot pfenniger84 r=4 p=0,90
### Warning [potrot]: Testing an iterative procedure: niter=10 eps=0.001000
4 0 0.352989 8
potrot pfenniger84 r=4 p=0,90 eps=0.0001 niter=20
4 0 0.352822 12
```

```07-Feb-05    V0.1 Created    PJT