Computational dynamics for N-body systems with conserving algorithms

This paper provides new and different perspectives dealing with computational dynamics for N-body systems and the associated conserving algorithms by design. In contrast to the traditonal setting of Newtonian mechanics with vector formalism where most developments are routinely conducted, and also in contrast to other frameworks with scalar formalism such as Lagrangian and Hamiltonian, the paper introduces new avenues and computationally convenient and attractive alternatives via the so-called Total Energy framework in configuration space. A measurable built in scalar descriptive function is employed via the Total Enery framework which is very natural for numerical discretizations to be routinely conducted, and it provides good and improved physical insight and computationally attractive features. In particular, although the equivalences of the various frameworks can be shown for holonomic-sceleronomic systems, the focus of this expositon and equivalences and the developments underlying conserving algorithms by design are strictly limited to the additonal restrictions, namely, the mass matrix is constant and the kinteic energy is not dependent upon the generalized coordinates. Past efforts via various original methods of development can be also be readily explained, and various conserving algorithms by design are presented with simple illustrative examples.