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Abstract: A general calculation method of calculating the spectrum of Lyapunov exponents is presented for n-dimensional nonlinear non-smooth systems by using the Poincaré map method. The Poincaré map is constructed by means of local maps to avoid calculating the Jacobian matrices at non-smooth points. The calculation of the spectrum of Lyapunov exponents for impact-vibrating systems with rigid constraints is given in detail. This method can be generally applied to systems with rigid or flexible (that is, perfectly elastic) constraints. In order to show the validity of this method, the spectrums of Lyapunov exponents are calculated in a large range of parameters for two given dynamical systems with rigid constraints and used to predict the dynamic behaviour. [Copyright &y& Elsevier]

The existence of rub-impact periodic motions in an eccentric rotor system is considered. A criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub-impacts are also discussed. A method consisting of analytical and numerical techniques is presented to solve the existence problem of rub-impact periodic motions. Some special results are obtained by theoretical analyses for rub-impact rotor systems, including the existence of grazing circle motions and that of single-impact periodic motions. [Copyright &y& Elsevier]

Abstract: A family of fourth and second-order accurate numerical schemes is presented for the solution of fifth-order boundary-value problems with two-point-boundary conditions. The non-polynomial sextic spline functions are applied to construct the numerical algorithms. This approach generalizes polynomial spline algorithms, and provides solution at every point of range of integration. Convergence of the methods is discussed through standard convergence analysis. A numerical illustration is given to show the pertinent features of the technique. [Copyright &y& Elsevier]