Numerical integration of multibody system dynamic equations using the coordinate partitioning method in an implicit Newmark scheme

The modelling of constrained multibody systems has been widely studied, published and implemented into computer programs, using different formalisms and terminologies. The resulting equations are formally of a mixed nature, viz. differential-algebraic, and cannot be directly solved by classical integrator schemes. Among the various techniques proposed for solving differential-algebraic equations, none exhibits a real superiority in terms of reliability, generality and efficiency. Depending on subjective criteria related to his applications, the 'user' has to select the most suitable method among several whose range of application is limited: indeed most of the time, this choice is 'problem dependent'. This paper proposes a method which conjointly takes advantage of the Coordinate Partitioning method and of the suitability of an implicit integration scheme regarding multibody systems containing flexible bodies. The top priority underlying this contribution is the rigorous resolution of the constraints during the simulation, whatever the application to be analysed.