简介：Inmechanics,bothclassicalandquantum,onestudiestheprofoundinteractionbetweentwotypesofenergy,namely,thekineticenergyandthepotentialenergy.Theformercanbeorganizedasthekinematicmetricontheconfigurationspacewhilethelattercanberepresentedbyasuitablepotentialfunction,suchastheNewtonianpotentialincelestialmechanicsandtheCoulombpotentialinquantummechanicsofatomicandmolecularphysics.Inthispaper,theauthorstudiesthekinematicgeometryofn-bodysystems.Themainresultsaxe(i)theintroductionofacanonicalcoordinatesystemwhichrevealsthetotalamountofkinematicsymmetrybyanSO(З)×O(n-1)actioninsuchacanoniealcoordinaterepresentation;(ii)anindepthanalysisoftheabovekinematicsystembothinthesettingofclassicalinvarianttheoryandbythetechniqueofequivarjantRiemanniangeometry;(iii)aremarkablysimpleformulaforthepotentialfunctioninsuchacanonicalcoordinatesystemwhichrevealsthewell-fittingbetweenthekinematicsymmetryandthepotentialenergy.