  In this article, we introduce higher derivative Lagrangians of this form
$\alpha_1 A_{\mu}(x)\dot{x}^\mu$, $\alpha_2 G_{\mu}(x)\ddot{x}^\mu$, $\alpha_3
B_{\mu}(x)\dddot{x}^\mu$, $\alpha_4 K_{\mu}(x)\ddddot{x}^\mu$, $\cdots$, that
generalize the electromagnetic interaction to higher order derivatives. We show
that odd order Lagrangians describe interactions analog to electromagnetism
while even order Lagrangians are similar to gravitational interaction. From
this analogy, we formulate the concept of the generalized induction principle
assuming the coupling between the higher fields $U_{(n),\mu}(x),\ n\geq1$ and
the higher currents $j^{(n)\mu}=\rho(x)d^nx^{\mu}/ds^n$, where $\rho(x)$ is the
spatial density of mass ($n$ even) or of electric charge ($n$ odd). In short,
this article is an invitation to reflect on a generalization of the concept of
force and of inertia. We discuss the implications of these paradigms more in
depth in the last section of the paper.
