Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism

Abstract EN

The slider-crank mechanism (SCM) is one of the mostimportant mechanisms in modern technology.

It appears in most combustionengines including those of automobiles, trucks, and other small engines.

TheSCM model considered here is an index-three nonlinear system ofdifferential-algebraic equations (DAEs), and therefore difficult to integratenumerically.

In this work, we present the application of the differentialtransform method (DTM) to obtain an approximate analytical solution of theSCM model in convergent series form.

In addition, we propose aposttreatment of the power series solution with the Padé resummationmethod to extend the domain of convergence of the approximate seriessolution.

The main advantage of the proposed technique is that it does notrequire an index reduction and does not generate secular terms or depend ona perturbation parameter.