Modeling flexible manipulators without inverting their mass matrices

In modern scientific literature, much attention is paid to optimal modeling of flexible dynamic systems. The importance of such studies is dictated by the ever-increasing demand of high-precision robotic manipulators and automatic mechanisms in the theory of control. This demand consists in the need for continuous adjustment of the movement of their effectors in real time, taking into account the compliance of the constituent links of these systems. The generalized Newton–Euler method formulated in this connection provides a reliable platform for the subsequent construction of modifications that accelerate the dynamic analysis of different classes of elastodynamic systems faster. A version of this method designed for optimal modeling of flexible manipulators is proposed that does not use the well-known procedure of inverting their mass matrices.