The aim of this work is to study some cases of stability of [image omitted] particularly in the case of non-conservative central attractive forces: [image omitted] In section 2, we define pseudo-conservative forces, generalize some well-known theorems in mechanics and obtain a necessary and sufficient condition for the existence of an energy-like first integral. In section 3, we obtain a non-trivial stable caseƒ(x)=(ρ +qx) 3ρ>0. In section 4, a necessary and sufficient condition for stability is obtained. The main result of this paper, that ƒεC1 andƒ“(0) exists, stability implies that 3ƒ“(0) = [2ƒ'(0)]2 is proved. This shows that the equilibrium, is generically unstable. In section 5, we generalize the results of section 2 for Lagrange's equations.
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