  This study explores the possibility and presents a methodology to synthesize
a classical mechanical analogue to the quantum mechanical 1D Kitaev model.
While being fundamentally different, we will identify significant conceptual
similarities between the two models that culminate in the occurrence, in the
classical analogue system, of topologically non-trivial bound states that are
akin to Majorana zero modes. By reformulating the Hamiltonian of the classical
system in a form reminiscent of second quantization, we show that a 1D
staggered classical mechanical chain can exhibit dynamic characteristics
analogous to the Kitaev's 1D superconducting model, as well as its
characteristic bound states. The non-trivial topological nature of the bound
states is further confirmed by the topological band structure analysis and by
the topological invariant. While the non-Abelian nature of these states remains
an open question, these results allow envisioning the possibility to achieve
topological braiding in classical mechanical systems.
