Distance

Description

The distance between the origins of frame_aand of frame_b are determined and provided at theoutput signal connector distance. Thisdistance is always positive. Derivatives of thissignal can be easily obtained by connecting theblockModelica.Blocks.Continuous.Derto "distance" (this block performs analytic differentiationof the input signal using the der(..) operator).

In the following figure the animation of a Distancesensor is shown. The light blue coordinate system isframe_a, the dark blue coordinate system is frame_b, andthe yellow arrow is the animated sensor.

If the distance is smaller as parameter s_small (in the "advanced" menu),it is approximated such that its derivative isfinite for zero distance. Without such an approximation, the derivative wouldbe infinite and a division by zero would occur. The approximation is performedin the following way: If distance > s_small, it is computed as sqrt(r*r) wherer is the position vector from the origin of frame_a to the origin of frame_b.If the distance becomes smaller as s_small, the "sqrt()" function is approximatedby a second order polynomial, such that the function value and its first derivativeare identical for sqrt() and the polynomial at s_small. Furthermore, the polynomialpasses through zero. The effect is, that the distance function is continuous anddifferentiable everywhere. The derivative at zero distance is 3/(2*s_small).