Nonlinear inerter in the light of Chua's table of higher-order electrical elements

The inerter, a recently discovered mechanical element, is analyzed from a broader perspective of Chua's periodical table of electric elements and electro-mechanical analogies. It is shown that the inerter can be reduced to today's generally accepted mechanical equivalent of electric capacitor or inductor only for a linear relationship between force and acceleration. The actual position of the inerter as a fundamental nonlinear mechanical element in a generalized effort-flow diagram is identified. Such identification is required for a correct modeling of the nonlinear behavior of systems which employ inerters of mechanical, electric or other nature.