Cubic spring with state \(q\in \mathbb R\) and parameters described below. The energy is

\begin{equation*} H(q) = \frac{F_1\,q^2}{2\,q_{ref}} + \frac{F_3\,q^4}{4q_{ref}^3}. \end{equation*}

The resulting force is:

\begin{equation*} f(q)= \frac{d \, H(q)}{d q} = F_1 \,\frac{q}{q_{ref}} + F_3 \, \frac{q^3}{q_{ref}^3}. \end{equation*}

so that \(f(q_{ref}) = F1+F3\).

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