Melnikov method for subharmonic orbits
The software below is the one used to compute the numerical results
presented in
The Melnikov method and subharmonic orbits in a piecewise-smooth
system . See the paper for details on the system and
parameters definition.
Download
subharmonic_melnikov.tar.gz
List of files, routines and their goals
-
system.dat contains system parameters: n m y0 t0 delta rho
omega, where
- nT is the period of the desired periodic orbit
-
2*m the number of impacts
-
y0 is the initial sead for the Newton method, such that (0,y0) is the
initial condition for an nT period orbit of the
unperturbed system
-
t0 is the zero of the modified Melnikov function
-
delta is perturbation parameter
-
rho is the ratio between the forcing and the restitution coefficient
omega is the frequency of the forcing
find_nm_ini_cond computes the initial conditions, (x0,t0) for
a periodic orbit whose parameters are given in system.dat
solve_wt0 computes a zero of the Melnikov function
find_delta_max.sh and follow_orbit.sh perform a
continuation method by increasing delta until the periodic orbit
bifurcates
find_existence_regions.sh computes the existence region for an
n,m-periodic orbit in the epsilon-r parameter space