Equilibrium and non-equilibrium dynamics of the cranio-mandibular complex and cervical spine

A dynamic model of the inverted pendulum characteristics of the head and cervical spine is presented. Using simple approximations and a single rotational-degree-of-freedom approach, the model is shown to conform to the classical mathematical description of an inverted pendulum motion. It also exhibits the well-known point of unstable equilibrium which is a standard property of such systems. Specific predictions of this theoretical description are compared against other values for the tilt, angular velocity and acceleration of the head during acceleration-sled testing, and with the Kapitza relation for mechanical-dither stabilization of an inverted pendulum. Numerical evaluations of the dynamic variables, resonant frequencies and time constants important to the problem are provided, and suggestions are made about how further results might be derived from extended versions of the model. This approach can now be refined to serve as a testing ground for analysing the biomechanics of traumatic neck injuries and for interpreting the possible roles that mandibular dysfunctions and dental malocclusion may play in disorders of the cervical spine. (Some background needed for exploring the latter possibility is presented.)