Relative acceleration from force and acceleration due to gravity¶
Suppose a reference frame \(S'\) is fixed to a moving body \(A\) (e.g. Earth). For some body \(B\) we can write a vector equation of motion relative to \(S'\) in the gravitational field of body \(A\) with the rotation of body \(A\) taken into consideration. From this, we can gather the meaning of the acceleration due to gravity, also known as the free fall acceleration: it is the acceleration of body \(B\) relative to \(S'\) in the absence of external forces (\(\vec F = 0\)) in the stationary case (the velocity of body \(B\) relative to \(S'\) is zero, i.e. \(\vec v = 0\) and \({\vec a}_\text{Cor} = 0\)).
- relative_acceleration¶
Vector of relative
accelerationof body \(B\) relative to \(S'\)
- Symbol:
a_rel- Latex:
\({\vec a}_\text{rel}\)
- Dimension:
acceleration
- Symbol:
F- Latex:
\({\vec F}\)
- Dimension:
force
- Symbol:
m- Latex:
\(m\)
- Dimension:
mass
- coriolis_acceleration¶
Vector of the Coriolis
accelerationof body \(B\).
- Symbol:
a_Cor- Latex:
\({\vec a}_\text{Cor}\)
- Dimension:
acceleration
- acceleration_due_to_gravity¶
Vector of the acceleration due to gravity.
- Symbol:
g- Latex:
\({\vec g}\)
- Dimension:
acceleration
- law¶
a_rel = g - a_Cor + F / m- Latex:
- \[{\vec a}_\text{rel} = {\vec g} - {\vec a}_\text{Cor} + \frac{{\vec F}}{m}\]