摘要
Inmechanics,bothclassicalandquantum,onestudiestheprofoundinteractionbetweentwotypesofenergy,namely,thekineticenergyandthepotentialenergy.Theformercanbeorganizedasthekinematicmetricontheconfigurationspacewhilethelattercanberepresentedbyasuitablepotentialfunction,suchastheNewtonianpotentialincelestialmechanicsandtheCoulombpotentialinquantummechanicsofatomicandmolecularphysics.Inthispaper,theauthorstudiesthekinematicgeometryofn-bodysystems.Themainresultsaxe(i)theintroductionofacanonicalcoordinatesystemwhichrevealsthetotalamountofkinematicsymmetrybyanSO(З)×O(n-1)actioninsuchacanoniealcoordinaterepresentation;(ii)anindepthanalysisoftheabovekinematicsystembothinthesettingofclassicalinvarianttheoryandbythetechniqueofequivarjantRiemanniangeometry;(iii)aremarkablysimpleformulaforthepotentialfunctioninsuchacanonicalcoordinatesystemwhichrevealsthewell-fittingbetweenthekinematicsymmetryandthepotentialenergy.
出版日期
1999年01月11日（中国期刊网平台首次上网日期，不代表论文的发表时间）
