Why the principles of inertia and of equivalence hold despite self-interaction

When self-interaction is included, the equation of motion without an external force yields solutions that violate the principle of inertia. This problem is a century old. Recently, it has been shown that there could also be solutions that violate the principle of equivalence. The present paper solves these problems by the observation that the dynamic part of the self-interaction is induced by the external force: there is no such interaction without an external force.