The position
![r](/media/stories/equations/classicalmechanics/pointkenetics01.gif.pagespeed.ce.dvcH4tce8S.gif)
![v](/media/stories/equations/classicalmechanics/pointkenetics02.gif.pagespeed.ce.ZILzqbK81S.gif)
![a](/media/stories/equations/classicalmechanics/pointkenetics03.gif.pagespeed.ce.V8mToA4ZbQ.gif)
![r = (x; y; z), v](/media/stories/equations/classicalmechanics/xpointkenetics04.gif.pagespeed.ic.KNK2Lz38G1.png)
The following holds:
![](/media/stories/equations/classicalmechanics/xpointkenetics05.gif.pagespeed.ic.pujmZZWN75.png)
When the acceleration is constant this gives:
![v(t) = v0 + at and s(t) = s0 + v0t](/media/stories/equations/classicalmechanics/xpointkenetics06.gif.pagespeed.ic.QCsKvWfQZF.png)
For the unit vectors in a direction perpendicular to the orbit
![et](/media/stories/equations/classicalmechanics/pointkenetics07.gif.pagespeed.ce.OPHVw0G4J-.gif)
![en](/media/stories/equations/classicalmechanics/pointkenetics08.gif.pagespeed.ce.IbwB2OZMOs.gif)
![](/media/stories/equations/classicalmechanics/xpointkenetics09.gif.pagespeed.ic.MpBhzcZW1x.png)
For the curvature k and the radius of curvature
![](/media/stories/equations/classicalmechanics/pointkenetics10.gif.pagespeed.ce.gCMVONFNgP.gif)
![](/media/stories/equations/classicalmechanics/xpointkenetics11.gif.pagespeed.ic.GrxA6_BMUz.png)
Polar coordinates
Polar coordinates are defined by:
![x = r cos( ), y = r sin( )](/media/stories/equations/classicalmechanics/xpointkenetics12.gif.pagespeed.ic.vVxp4CBkty.png)
![](/media/stories/equations/classicalmechanics/pointkenetics13.gif.pagespeed.ce.py1As2YTn6.gif)
The velocity and the acceleration are derived from:
![](/media/stories/equations/classicalmechanics/xpointkenetics14.gif.pagespeed.ic.qvt78ieuz2.png)