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/xpointdynamicsmoving01.gif.pagespeed.ic.irTE9R0Zrz.png)
- 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/xpointdynamicsmoving06.gif.pagespeed.ic.84SvzTBV1q.png)
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving07.gif.pagespeed.ic.h_08JABLPR.png)
The chain rule gives:
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving08.gif.pagespeed.ic.VTkt4wyVwv.png)
so:
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving09.gif.pagespeed.ic.G6OYtx6jeP.png)
This leads to:
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving10.gif.pagespeed.ic.G770CzrGsG.png)
Hence the Newtonian equation of motion
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving11.gif.pagespeed.ic.exrPhTCW6e.png)
will be transformed into:
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving12.gif.pagespeed.ic.D6J027sF7k.png)
The apparent forces are taken from he origin to the effect side in the way
![](/media/stories/equations/classicalmechanics/xpointdynamicsmoving13.gif.pagespeed.ic.a3txYEkkfd.png)