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potccd - Create an image with potentials or densities from a potential
potccd stores the potential
values of a potential descriptor (see potential(5NEMO)
) on a regular grid
in standard image(5NEMO)
format. It is also possible to store the Poissonian
density, either 2D or 3D. For this numerical derivatives of the force field
are used, and hence a small difference step needs to be given.
stored on a grid could be a good approach when the potential is expensive
to compute, though in orbit calculations this could limit the exact conservation
of the integrals of motion such as energy.
Irregular grids are not forbidden
(see x=,y=,z=) but the image(5NEMO)
WCS descriptor will then be invalid.
The following parameters are recognized in any order if the
keyword is also given:
ndim=2 the Z-coordinate is not ignored, and hence may give meaningless results
if forces depend on Z.
- Output file (image). No default.
of the potential(5NEMO)
. No default
- Parameters for the potential.
- Any optional data file associated with the potential.
to test potential at. This should be a regular array, e.g. 1:10:0.2. Default:
- Y-coordinate(s) to test potential at. Default: 0.
- Z-coordinate(s) to
test potential at. Default: 0.
- Time to test potential at
- Output mode. Choices are potential, accelerations in X, Y or Z, and density
(which needs dr>0). Default: pot.
- Difference step used to compute numerical
force derivates that are used to compute Poissonian densities.
this instead of any returned pattern speed. Default: not used, the first
parameter in potpars= is used.
- Number of dimensions used in Poissonian
density computation. Should be 2 or 3.
- Normally the density (mode=den)
is derived by first derivatives of the forces, but for some potentials
the force was never implemented (e.g. potname=gauss). In this case the 2nd
derivative of the potential will be needed, hence nder=2. Default: 1
First a somewhat obscure way in to create
a map of an arbitrary function using the potname=rotcur lookup table. It
will use a spline interpolation, and if mode=pot is used, the "potential"
is actually the "rotation curve" itself, since in general one cannot easily
compute the potential from a rotation curve without knowing the full geometry.
Here is an example how to create a smooth radial profile of the function
"f(x)=1/sqrt(4+x)" on a grid from -10..10:
% nemoinp 0:10 | tabmath - - ’1/(sqrt(4+%1)’ > map0.tab
% potccd map0 rotcur 0 map0.tab x=-10:10:0.1 y=-10:10:0.1
If the functional form is know, ccdmath(1NEMO)
will perhaps do better,
if not a little more involved to type.
Here is an example of an orbit integration
in the analytical plummer potential, and in two gridded versions of the
% mkorbit o1 1 1 0 -0.5 0 0 potname=plummer
% orbint o1 - 10000 0.01 ndiag=10000 | orblist - | tail -1
Energy conservation: 2.05084e-11
10000 100 -1.11384 -0.266207 0 0.557843 -0.315574 0
% potccd ccd1 plummer x=-2:2:0.01 y=-2:2:0.01
% orbint o1 - 10000 0.01 ndiag=10000 potname=ccd potfile=ccd1 | orblist - |
Energy conservation: 0.00223468
10000 100 -1.11427 -0.265478 0 0.557503 -0.315907 0
% potccd ccd2 plummer x=-2:2:0.0025 y=-2:2:0.0025
% orbint o1 - 10000 0.01 ndiag=10000 potname=ccd potfile=ccd2 | orblist - |
Energy conservation: 0.000609561
10000 100 -1.11385 -0.266169 0 0.557829 -0.315593 0
10-Jun-92 V1.0 Created PJT
30-mar-94 V1.1 added density options (dr=, ndim=) PJT
12-sep-02 V1.2 added mode= PJT
19-mar-2021 V2.1 added nder= PJT
9-jan-2022 V2.2 fixed WCS, updated examples PJT
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