The total force in a moving coordinate system can be found by subtracting the apparent forces from the forces working in the reference frame:
![F = F -F(app)](/media/stories/equations/classicalmechanics/pointdynamicsmoving01.gif)
- 1. Transformation of the origin:
- 2. Rotation:
- 3. Coriolis force:
- 4. Centrifugal force:
Tensor notation
Transformation of the Newtonian equations of motion to![](/media/stories/equations/classicalmechanics/pointdynamicsmoving06.gif)
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving07.gif)
The chain rule gives:
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving08.gif)
so:
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving09.gif)
This leads to:
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving10.gif)
Hence the Newtonian equation of motion
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving11.gif)
will be transformed into:
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving12.gif)
The apparent forces are taken from he origin to the effect side in the way
![](/media/stories/equations/classicalmechanics/pointdynamicsmoving13.gif)