Five-body choreography on the algebraic lemniscate is a potential motion

Publication date: Available online 7 March 2019Source: Physics Letters AAuthor(s): Juan Carlos Lopez VieyraAbstractIn a remarkable paper of 2003 by Fujiwara et al. [1], a figure-eight three-body choreography on the algebraic lemniscate of Bernoulli was discovered. Such a choreography was found to be driven by the action of a pairwise potential V(rij), depending only on the mutual relative distances rij, i,j=1,2,3. In the present Letter we show that two different choreographies of five bodies on the same algebraic lemniscate exist and correspond to solutions of ten coupled Newton equations of motion with a pairwise interaction potential. For each choreography the explicit form of the potential is found and ten constants of motion are presented, thus, it is superintegrable.

Source: Physics Letters A - March 8, 2019 Category: Physics Source Type: research