I'm working through a textbook and it includes the equation

$m \ddot{x} + m \gamma \dot{x} = \frac{-du}{dx}+\xi(t) $.

It says that we can "neglect the inertial term" from this for the next step. Which is the inertial term, and why is it called that?

## Best Answer

In your expression, the term $m\ddot x$ is the "inertial term".

It describes the force needed to accelerate ($\ddot x$) the mass $m$. Hence, "inertial".

It can be neglected if you know that that term is small compared to other terms in the expression (for example, the velocity term with $\dot x$ in it). That depends on the context.