In a polar coordinate system (r, θ), the position error is calculated as 2*sqrt(r^2 + (r0)^2 - 2*r*r0*cos(Δθ)) where r is the measured radial distance, r0 is the nominal radial distance, and Δθ is the difference between the measured and the nominal angle.
In a Cartesian coordinate system (x, y), the position error is calculated as 2*sqrt((Δx)^2 + (Δy)^2) where Δx and Δy are the deviations from nominal in the X and Y axes, respectively.
No problem. The quickest way to derive it is by using the law of cosines, but you can also derive it using the Cartesian formula and by letting x = r*cosθ and y = r*sinθ for each point (different r and different θ), substituting, and eventually using the cosine of a difference identity.
No problem. The quickest way to derive it is by using the law of cosines, but you can also derive it using the Cartesian formula and by letting x = r*cosθ and y = r*sinθ for each point (different r and different θ), substituting, and eventually using the cosine of a difference identity.
