Linear-rotational Analogs - Galilean Frame Transforms

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'.
A = (Variable) relative acceleration between two accelerating frames F and F'.

 Relative position

Relative velocity

Equivalent accelerations

 Relative accelerations

Apparent/fictitious forces
Rotation

Ω = Constant relative angular velocity between two frames F and F'.
Λ = (Variable) relative angular acceleration between two accelerating frames F and F'.

 Relative angular position

Relative velocity

Equivalent accelerations

 Relative accelerations

Apparent/fictitious torques
Transformation of any vector T to a rotating frame

Read more about this topic:  Linear-rotational Analogs

Famous quotes containing the words galilean, frame and/or transforms:

    “Last came, and last did go,
    The pilot of the Galilean lake.”
    —John Milton (1608–1674)

    “The heroes and discoverers have found true more than was previously believed, only when they were expecting and dreaming of something more than their contemporaries dreamed of, or even themselves discovered, that is, when they were in a frame of mind fitted to behold the truth. Referred to the world’s standard, they are always insane. Even savages have indirectly surmised as much.”
    —Henry David Thoreau (1817–1862)

    “It is old age, rather than death, that is to be contrasted with life. Old age is life’s parody, whereas death transforms life into a destiny: in a way it preserves it by giving it the absolute dimension. ... Death does away with time.”
    —Simone De Beauvoir (1908–1986)