On the dynamics equations of systems of interconnected bodies

Abstract

A method is elucidated for deriving the equations of motions of mechanical systems comprised of an arbitrary number of absolutely solid bodies containing both closed and open links. The method proposed is universal in nature and convenient for algorithmization and programming on electronic computers. The method proposed in /1/ is most general for the description of systems of many bodies with the structure of interconnections with closed links. Its essential disadvantage is, however, the lack of a formal apparatus to describe the couplings in the system and the incomplete utilization of information about the relative motion in the adjacent bodies due to discarding part of the hinges during transformation of the system with closed links into a system with the structure of a tree. The method elucidated below to derive the dynamical equations can be applied to mechanical systems that are sets of bodies connected by holonomic and non-holonomic, scleronomic, and rheonomic constraints. It is assumed that the system of interconnections is such that a system that does not contain a closed link can be obtained by a single slash of the pertinent bodies. To simplify the exposition, the method is demonstrated on scleronomic holonomic systems, often encountered in practice. The proposed method is a development of the formalism elucidated in /2/.