Mechanical model of carbon dioxide vibrational spectrum

Classical dynamics methods have been used to study the nonlinear vibrations of a CO$_2$ molecule. Consideration includes not only the anharmonicity valence angle, which enables one to explain the Fermi resonance, but also the physical nonlinearity of the force field (stiffness and softness of springs). In the farthest neighbor approximation (with regard to oxygen–oxygen interaction), a set of nonlinear differential equations in the Lagrangian form has been derived. Their analytical solution has been derived using the method of invariant normalization. The occurrence of a strange attractor has been discovered by numerical simulation. Recommendations for the selection of initial conditions are given that take into account the possibility of regular beatings that change into to chaotic beatings.