For discrete systems the *Hamilton principle* yields the *Lagrangian equations*

where the *Lagrangian* is the difference between the kinetic energy and the potential energy, i.e.*L* = *T* − *V*. The *Hamiltonian* is given by , where .

If *η*_{i} is the displacement of particle *i* from its equilibrium position (see figure D.1), then

where *a* is the separation distance between the equilibrium positions of two neighboring ...

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