  We discuss the consequences of higher derivative Lagrangians of the form
$\alpha_1 A_{\mu}(x)\dot{x}^\mu$, $\alpha_2 G_{\mu}(x)\ddot{x}^\mu$, $\alpha_3
B_{\mu}(x)\dddot{x}^\mu$, $\alpha_4 K_{\mu}(x)\ddddot{x}^\mu$, $\cdots$,
$U_{(n)\mu}(x)x^{(n)\mu}$ in relativistic theory. After establishing the
equations of the motion of particles in these fields, we introduce the concept
of the generalized induction principle assuming the coupling between the higher
fields $U_{(n),\mu}(x),\ n\geq1$ with the higher currents
$j^{(n)\mu}=\rho(x)x^{(n)\mu}$, where $\rho(x)$ is the spatial density of mass
or of electric charge. In addition, we discuss the analogy of the field
$G_\mu(x)$ with the gravitational field and its inclusion in the general
relativity framework in the last section. This letter is an invitation to
reflect on a generalisation of the concept of inertia and we also discuss this
problem in the last section.
