Two Masses in Relative Hooke’s Potential and Elliptic Integrals

Abstract We consider the relative motion of system two masses connected by a spring. analyze it in range Hooke’s law and show that equations are nonlinear once equilibrium length spring is nonzero. Although way deriving standard classical mechanics solving them complicated interesting problem mathematical physics. The analysis leads naturally to elliptic integrals. obtain complete formulas an interesting, from both physical point view, way. Our might be useful some problems molecular dynamics diatomic molecules.