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:
- 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