Central configurations of the n-body problem with a general force function. I - Fundamental equations and theoretical analysis

The central configurations of the n-body system in an inverse k (other than 1) force field is investigated using a method different from those of Palmore (1973, 1975, 1976, 1977) and Saari (1975, 1980). An extension of the main results concerning the central configuration in a gravitational field is presented. The derivation of the equations of central configurations, with mutual distances as the unknowns, is illustrated.