On the<i>n</i>-body problem in R4
On the<i>n</i>-body problem in R4
Using geometric mechanics methods, we examine aspects of the dynamics of n mass points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:math> with a general pairwise potential. We investigate the central force problem, set up the n -body problem and discuss certain properties of relative equilibria. We describe regular n -gons in <mml:math …