Estimation of Lyapunov exponents from multibody dynamics in differential-algebraic form

This article discusses the estimation of Lyapunov characteristic exponents related to the solution of non-linear multibody dynamics problems expressed in the form of systems of differential–algebraic equations. Current literature on the topic projects the differential–algebraic equations in the state space of the underlying strangeness free ordinary differential equations. This article shows how Lyapunov exponents can be successfully estimated with the discrete QR method directly applied to the matrix pencil associated to the differential–algebraic equations, using algorithmically dissipative multistep methods. Numerical results show the soundness of the proposed approach.