Galilean Frame Transforms
For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative accelerations.
| Motion of entities | Inertial frames | Accelerating frames |
|---|---|---|
| Translation
V = Constant relative velocity between two inertial frames F and F'. |
Relative position Relative velocity |
Relative accelerations Apparent/fictitious forces |
| Rotation
Ω = Constant relative angular velocity between two frames F and F'. |
Relative angular position Relative velocity |
Relative accelerations Apparent/fictitious torques |
| Transformation of any vector T to a rotating frame |
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Read more about this topic: Linear-rotational Analogs
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