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Point kinetics in a fixed coordinate system

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Physics Formulary – Mechanics - Point-kinetics in a fixed coordinate system.

Definitions


The position r the velocity v and the acceleration a are defined by:
r = (x; y; z), v

The following holds:


When the acceleration is constant this gives: v(t) = v0 + at and s(t) = s0 + v0t
For the unit vectors in a direction perpendicular to the orbit et and parallel to it en holds:


For the curvature k and the radius of curvature holds:



Polar coordinates


Polar coordinates are defined by: x = r cos( ), y = r sin( ). So, for the unit coordinate vectors holds:


The velocity and the acceleration are derived from:
 
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