The parameters below are used to drive the bouncing ball in this Autodesk Inventor 2012 model. Dx and Dy are x- and y-axis mate constraint offsets from the origins of a hidden part. Dx is the independent variable that is changed by the drive constraint, or animated in Inventor Studio. Dy is the dependent variable that is calculated from Dx. Dx is converted to a unitless value (DxUl) before any calculations. Once the calculations are completed, the new y-value is converted back to millimeters to become Dy. The squared function will not work on lengths because it squares the unit to become area (square millimeters).
Spacing is the distance between bounces.
Height is the height of the parabola on the first bounce.
DxPrime is the conversion of the X-axis values to repeating values from 0-to-Spacing (using the modulo operation) and then the conversion of those value to -spacing/2-to-spacing/2, or in the case below repeating values of 0-to-55 converts to -28-to-27.
DyScaled squares DxPrime then scales it up or down so the parabola fits the desired height defined by Height.
DyDecayed scales down the parabolas 1/n so that the second parabola is only half the height of the first, the third parabola is only one third the height of the first, etc.
DyLeveled lowers the parabolas so that they all bounce at the same vertical value. Without this, all the vertices are level so that the ball appears to climb a hill.
Thanks to Bill Fane for helping us navigate through the different possible ways to approach this animation including many failed attempts to apply Transitional Constraints along a parabolic path.