section_path: Description of objects and their motion/Kinematics/Frames of reference
section_name: Frames of reference
paragraph_text: Frames of reference
  
  While the position, velocity and acceleration of a particle can be described with respect to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames. An inertial frame is an idealized frame of reference within which an object with zero net force acting upon it moves with a constant velocity; that is, it is either at rest or moving uniformly in a straight line. In an inertial frame Newton's law of motion, F = m a {\displaystyle F=ma}, is valid.
  
  Non-inertial reference frames accelerate in relation to another inertial frame. A body rotating with respect to an inertial frame is not an inertial frame. When viewed from an inertial frame, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it appears that there are other forces that enter the equations of motion solely as a result of the relative acceleration. These forces are referred to as fictitious forces, inertia forces, or pseudo-forces.
  
  Consider two reference frames S and S'. For observers in each of the reference frames an event has space-time coordinates of (x, y, z, t) in frame S and (x', y', z', t') in frame S'. Assuming time is measured the same in all reference frames, if we require x = x' when t = 0, then the relation between the space-time coordinates of the same event observed from the reference frames S' and S, which are moving at a relative velocity u in the x direction, is:
  
  This set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform). This group is a limiting case of the Poincaré group used in special relativity. The limiting case applies when the velocity u is very small compared to c, the speed of light.
  
  The transformations have the following consequences:
  
  For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious centrifugal force and Coriolis force.