5.5.4 Analysis

• orbstat is an example of a simple program that reads orbits, and displays statistics of it's 2D (x-y-) coordinates: maximum extent, as well as statistics of the angylar momentum. This program is not suited for 3D orbits yet.

  % orbint orb1 orb1.long 
  % orbstat orb1.out
  # T     E       x_max   y_max   u_max   v_max   j_mean  j_sigma
  1000 -0.687107 1 0.999958 0.746764 0.746611 0.2 3.83111e-09
  

• orbfour performs a variety of fourier analysis on the

  % orbint orb1 orb1.long 100000 0.01 10000 10 plummer 
  INIPOTENTIAL Plummer: [3d version]
  Pattern speed=0
  0.000000 0.020000 -0.707107     -0.6871067811865
  100.000000 0.277794 -0.964901     -0.6871067811856
  200.010000 0.020912 -0.708019     -0.6871067812165
  300.020000 0.271222 -0.958329     -0.6871067812194
  400.030000 0.023376 -0.710483     -0.6871067812465
  500.040000 0.259253 -0.946360     -0.6871067812551
  600.050000 0.027415 -0.714522     -0.6871067812765
  700.060000 0.242979 -0.930086     -0.6871067812904
  800.070000 0.033056 -0.720163     -0.6871067813065
  900.080000 0.223694 -0.910801     -0.6871067813241
  Energy conservation: 2.00138e-10                               
  % orbfour orb1.long amode=t
  <R> N A0 A1 A2 A3 A4 B1 B2 B3 B4
  1 10001 0.000360461 0.334714     0.000150399 -0.000472581 -0.000158864
                     -0.000667155  0.000228086 -0.000725406  0.000103029
  
  % orbfour orb1.long amode=f
  <R> N C0 C1 P1 C2 P2 C3 P3 C4 P4
  1 10001 0.000360461 
          0.334715      -0.114202 
          0.000273209   56.5992 
          0.000865763 -123.083
          0.000189349  147.035
  

• orbsos computes surface of section coordinates. Since this program does not plot, but produces a simple ascii table, you can pipe the output into tabplot:

  % orbsos orb1.long y | tabplot - 3 4  xlab=Y ylab=VY
  % orbsos orb1.long x | tabplot - 3 4  xlab=X ylab=VX
  

  will plot either a Y-VY or X-VX surface of section.

  Figure: Surface of Section for sample orbit 1 (orb1.long)

  

• orbdim computes the dimensionality of an orbit, i.e. how many integrals of motions it has. Although it requires very long integration times to accurately compute this, it is completely automatic, and does not require an analysis like that for a surface of section (which is also graphic). It is based on an interesting paper by Carnevali & Santangelo^5.15.

• otos transforms an orbit back into a snapshot, thereby giving you the much richer set of analysis tools that are available for snapshot's.