From multi-body to many-body dynamics

This article provides a brief historical review of multi-body dynamics analysis, initiated by the Newtonian axioms through constrained (removed degrees of freedom) Lagrangian dynamics or restrained (resisted degrees of freedom) Newton–Euler formulation. It provides a generic formulation method, based on system dynamics in a reduced configuration space, which encompasses both the aforementioned methods and is applicable to any cluster of material points. A detailed example is provided to show the integration of other physical phenomena such as flexibility and acoustic wave propagation into multi-body dynamics analysis. It is shown that in the scale of minutiae, when the action potentials deviate from Newtonian laws, the forces are often described by empirical or stochastic functions of separation and the medium of interactions. These make for complex analyses and distinguish a host of many body problems from Newtonian laws of motion. A simple example is provided to demonstrate this. It is suggested that unification of many-body analysis with that of multi-body dynamics is incumbent on the fundamental understanding of interaction potentials at close separations.