Routines for the computations of periodic orbits using Melnikov and Newton method in a piecewise-smooth system (the rocking block with restitution coefficient)

Collection of C and bash routines for the computation of periodic orbits via Melnikov method in a piecewise-smooth system This software is the one used to compute the numerical results presented in The Melnikov method and subharmonic orbits in a piecewise-smooth system .

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 seed 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