Numerical study of a forced pendulum with friction

We first describe the model of a forced pendulum with viscous damping and C oulomb friction. Then we show that a unique local solution of the mathemati cally well-posed problem exists. An adapted numerical scheme is built. Atte ntion is devoted to the study of the nonlinear behaviour of a pendulum via a numerical scheme with small constant time steps. We describe the global b ehaviour of the free and forced oscillations of the pendulum due to frictio n. We show that chaotic behaviour occurs when friction is not too large. Ly apunov exponents are computed and a Melnikov relation is obtained as a limi t of regularised Coulomb friction. For larger friction, asymptotic behaviou r corresponds to equilibrium.