Einstein force

The Einstein force is an apparent force which acts in an accelerated reference system.

Suppose that there are two reference frames S and S ', where S ' is moving relative to S. The origin of S ' moves along some curve in S, which can be traced out by some vector C which is a function of t. The Einstein force is the apparent force acting on a particle of mass m in the S ' frame, and is defined by

${\displaystyle {\textbf {F}}=-m{d^{2}{\textbf {C}} \over dt^{2}}.}$