inertialsystem

An inertialsystem, or inertial frame of reference, is a coordinate system in which a body not acted upon by external forces moves at a constant velocity in a straight line. In such a frame, Newton's first law holds: a body at rest stays at rest, and a body in motion continues with uniform motion unless a net external force acts on it. Equivalently, the laws of mechanics have the same form in all inertial frames. In classical (Newtonian) mechanics, inertial frames are related by Galilean transformations. In special relativity, inertial frames are related by Lorentz transformations, which preserve the form of physical laws across observers moving at constant relative velocity.

In general relativity, there is no global inertial frame in curved spacetime, but locally one can approximate a freely falling region as an inertial frame. This leads to the concept of locally inertial frames, where, over a small enough neighborhood, the effects of gravity can be neglected and laws of physics reduce to those of special relativity.

A key distinction is between inertial and non-inertial frames. Non-inertial (accelerating) frames give rise to fictitious or pseudo-forces, such as the centrifugal force on a rotating platform or the feeling of acceleration in a car that speeds up. The presence of such fictitious forces signals that the frame is non-inertial. In practice, laboratory frames on Earth are approximately inertial for many experiments, with small corrections from Earth's rotation, gravity, and translational accelerations.

Historically, the concept emerges from Galileo’s thought experiments and Newton’s formulation of mechanics. Today, inertial frames are fundamental to classical mechanics and remain essential for analyzing physical systems across physics, engineering, and navigation.