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Rocking block integrator



How to execute

Assume you have successfully compiled the source. It has to be executed from the command line, just typing:
./main_single_block x0 y0 t0 epsilon numiterates maximpacts
where: The values of the frequency of the forcing and the restitution coefficient have to be set in the file "system_params.dat".

What will (should) the program do?

It will integrate the system until one of the following things occur:
  1. The number of iterations by the strobosopic map reaches numiterates
  2. The number of iterations of the impact map reaches maximpacts
  3. The trajectory escapes to infinity. There is an internal parameter ("stop_tol") to decide this (see below).
Note that the first condition, 1., 2. or 3., that occurs will stop the program. Hence, if one wishes necessary to compute an given number of iterations of the stroboscopic map then set "maximpacts" to a very high value to ensure that 1) occurs first (similarly for the impact map).

What will the program return?

The program will create three files: All three files will contain three columns: x y t
Note that these three files are removed at each execution. Make copies of them if you want to keep data.

How can I plot the results?

Gnuplot is an excellent option, but matlab would do the trick to. There may be thousands of other options.

What parameters can be (easily) changed/tuned?

Basically all of them. These are set in the preamble of the file "main_single-block.cpp", and refer to plotting options, integration options, tolerances for the Newton method and stopping conditions. Note that if any is changed then to the program has to be recompiled. All of them are described in the preamble of the main program. Of course, the frequency (omega) and restitution coefficient (r), which are given in the system_params.dat file can be changed at any time without recompiling. Also the perturbation parameter (epsilon), the initial conditions and the maximum number of iterates for the maps can be also changed as desired, as they are the input parameters when calling the main program. Note that, in principle, there is no need to change anything in the "integrate_single-block.cpp" file, which contains the machinery.

Where are the differential equations written?

These are also given in "main_single-block.cpp", just before the main program starts. Non of the routines are using any property for these equations, so they can be replaced by other ones, for instance the non-linear ones. One can also of course change the forcing too.