Differential equations and dynamical systems
Differential equations and dynamical systems
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
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In this work we present two systems with non-linear neo-Hookean components. In such systems there always exists an element with a non-linear characteristic equation. This element can be considered to be a rubber or another equivalent structure. We shall prove that the utilization of a neo-Hookean element will not destroy the properties of the structure, but it riches these properties and it could be a good solution in many cases. The first model describes a quarter of an automobile and the second one is dedicated to a half-automobile model. We obtain the equilibrium positions, study their stability in the most general case and for the first model we also discuss the stability of the motion. In the paper there are also numerical applications.