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We study a classical model of isosceles triatomic "A-B-A" molecules. Theatoms, considered mass points, interact mutually via a genericrepulsive-attractive binary potential.  First we show that the steady states, or relative equilibria (RE),corresponding to rotations about the molecule symmetry axis may be determinedqualitatively assuming the knowledge of 1) the shape of the binary interactionpotential, 2) the equilibrium diatomic distances (i.e., the equilibrium bondlength) of the A-A and A-B molecules, and 3) the distance at which the RE ofthe diatomic A-A molecule ceases to exist. No analytic expression for theinteraction potentials is needed.  Second we determine the stability of the isosceles RE modulo rotations usinggeometric mechanics methods and using Lennard-Jones diatomic potentials. As aby-product, we verify the qualitative results on RE existence and bifurcation.For isosceles RE we employ the Reduced Energy-Momentum method presented in[J.E. Marsden, Lectures in Mechanics, Cambridge University Press, 1992],whereas for linear (trivial isosceles) RE we apply the Symplectic Slice method,a technique based on the findings in the paper [R.M. Roberts, T. Schmah and C.Stoica, Relative equilibria for systems with configurations space isotropy, J.Geom. Phys., 56, 762, (2006)].

Notes on relative equilibria of isosceles molecules in classical approximation