ABSTRACT
Strong-force potentials are easy to deal with in order to show the existence of choreographies. Given existence results there remains the problem of how to find choreographies explicitly. The simplest choreographies have one or several symmetries. The existence of the choreographies and the variety of patterns they display comes as a surprise, especially in what concerns complicated or even asymmetric patterns. Every piece of the N-body problem people start to understand opens a new world of questions. A natural question is to ask if, beyond the N-gon solutions, there are other solutions of the N-body problem with all masses equal, either planar or spatial such that all the bodies move along the same path. The N-gon solutions will be considered as the trivial choreographies. The N-gon solutions offer an interesting aspect: all bodies move periodically, tracing the same curve on the plane, with a constant time interval between the passage of one body and the next at any particular point.
