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)

    “In this choice of inheritance we have given to our frame of polity the image of a relation in blood; binding up the constitution of our country with our dearest domestic ties; adopting our fundamental laws into the bosom of our family affections; keeping inseparable and cherishing with the warmth of all their combined and mutually reflected charities, our state, our hearths, our sepulchres, and our altars.”
    —Edmund Burke (1729–1797)

    “Now, since our condition accommodates things to itself, and transforms them according to itself, we no longer know things in their reality; for nothing comes to us that is not altered and falsified by our Senses. When the compass, the square, and the rule are untrue, all the calculations drawn from them, all the buildings erected by their measure, are of necessity also defective and out of plumb. The uncertainty of our senses renders uncertain everything that they produce.”
    —Michel de Montaigne (1533–1592)