Acceleration of transfer between relative frames

Imagine two reference frames, one of which is fixed (\(S\)) and the other one is moving (\(S'\)). The motion of a body stationary in moving frame \(S'\) due to the motion of the frame itself is called transfer motion. The acceleration related to such motion is called transfer acceleration. It is composed of the acceleration of the moving frame relative to the fixed frame, centripetal acceleration and the acceleration due to uneven rotation of the moving frame. The transfer acceleration only depends on the motion of frame \(S'\) relative to stationary frame \(S\), so its physical meaning would be that it is the acceleration in \(S\) of a point stationary in \(S'\).

Links:

  1. Wikipedia.

transfer_acceleration_law(moving_frame_acceleration_, centripetal_acceleration_, rotation_acceleration_)[source]

Transfer acceleration as a sum of accelerations.

Law:

a_tr = a_0 + a_cp + a_rot

Latex:
\[{\vec a}_\text{tr} = {\vec a}_0 + {\vec a}_\text{cp} + {\vec a}_\text{rot}\]
Parameters:
  • moving_frame_acceleration_

    acceleration of \(S'\) relative to \(S\)

    Symbol: a_0

    Latex: \({\vec a}_0\)

    Dimension: acceleration

  • centripetal_acceleration_

    centripetal acceleration of body in \(S'\)

    Symbol: a_cp

    Latex: \({\vec a}_\text{cp}\)

    Dimension: acceleration

  • rotation_acceleration_

    acceleration caused by non-uniform rotation of \(S'\)

    Symbol: a_rot

    Latex: \({\vec a}_\text{rot}\)

    Dimension: acceleration

Returns:

transfer acceleration of body

Symbol: a_tr

Latex: \({\vec a}_\text{tr}\)

Dimension: acceleration

moving_frame_acceleration_law(transfer_acceleration_, centripetal_acceleration_, rotation_acceleration_)[source]

Acceleration of \(S'\) relative to \(S\).

Law:

a_0 = a_tr - (a_cp + a_rot)

Latex:
\[{\vec a}_0 = {\vec a}_\text{tr} - ({\vec a}_\text{cp} + {\vec a}_\text{rot})\]
Parameters:
  • transfer_acceleration_

    transfer acceleration of body

    Symbol: a_tr

    Latex: \({\vec a}_\text{tr}\)

    Dimension: acceleration

  • centripetal_acceleration_

    centripetal acceleration of body in \(S'\)

    Symbol: a_cp

    Latex: \({\vec a}_\text{cp}\)

    Dimension: acceleration

  • rotation_acceleration_

    acceleration caused by non-uniform rotation of \(S'\)

    Symbol: a_rot

    Latex: \({\vec a}_\text{rot}\)

    Dimension: acceleration

Returns:

acceleration of \(S'\) relative to \(S\)

Symbol: a_0

Latex: \({\vec a}_0\)

Dimension: acceleration

centripetal_acceleration_law(transfer_acceleration_, moving_frame_acceleration_, rotation_acceleration_)[source]

Centripetal acceleration in \(S'\).

Law:

a_cp = a_tr - (a_0 + a_rot)

Latex:
\[{\vec a}_\text{cp} = {\vec a}_\text{tr} - ({\vec a}_0 + {\vec a}_\text{rot})\]
Parameters:
  • transfer_acceleration_

    transfer acceleration of body

    Symbol: a_tr

    Latex: \({\vec a}_\text{tr}\)

    Dimension: acceleration

  • moving_frame_acceleration_

    acceleration of \(S'\) relative to \(S\)

    Symbol: a_0

    Latex: \({\vec a}_0\)

    Dimension: acceleration

  • rotation_acceleration_

    acceleration caused by non-uniform rotation of \(S'\)

    Symbol: a_rot

    Latex: \({\vec a}_\text{rot}\)

    Dimension: acceleration

Returns:

centripetal acceleration of body in \(S'\)

Symbol: a_cp

Latex: \({\vec a}_\text{cp}\)

Dimension: acceleration

rotation_acceleration_law(transfer_acceleration_, moving_frame_acceleration_, centripetal_acceleration_)[source]

Acceleration due to non-uniform rotation of \(S'\).

Law:

a_rot = a_tr - (a_0 + a_cp)

Latex:
\[{\vec a}_\text{rot} = {\vec a}_\text{tr} - ({\vec a}_0 + {\vec a}_\text{cp})\]
Parameters:
  • transfer_acceleration_

    transfer acceleration of body

    Symbol: a_tr

    Latex: \({\vec a}_\text{tr}\)

    Dimension: acceleration

  • moving_frame_acceleration_

    acceleration of \(S'\) relative to \(S\)

    Symbol: a_0

    Latex: \({\vec a}_0\)

    Dimension: acceleration

  • centripetal_acceleration_

    centripetal acceleration of body in \(S'\)

    Symbol: a_cp

    Latex: \({\vec a}_\text{cp}\)

    Dimension: acceleration

Returns:

acceleration caused by non-uniform rotation of \(S'\)

Symbol: a_rot

Latex: \({\vec a}_\text{rot}\)

Dimension: acceleration