Key Concept:It is convenient in kinematics to express velocities
and accelerations in terms of components in different coordinate systems or
in kinetics to express forces with different components
associated
with different coordinate systems. Transformation of coordinates allows you
to do so.
The
figure below shows a particle, P, described by three coordinate systems
with unit vectorsiand
j,erand eθ,anden andet. The objective is to be able to express
the unit vectors iand jin terms oferand eθ(or
vice-versa) oriand jin terms ofen and et(or vice-versa).
To
transform fromereθtoijdrop perpendiculars fromitoerandj toeθand use
