continuous curvature for piecewise function?[execute entire worksheet !!! first, then scroll back to top]
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track initially curves up, then straightens out from the origin and then curves down to join at the point (1,1), with an inflction point in the middle. The curvature on the concave up segment gets larger than that on the concave down segment.
Stewart Calculus 8e 13.R.24 Imagine a horizontal train track path. It would be important to make sure the sideways impulse from a jump in curvature be removed by designing a path with continuous curvature, and also make sure the curvature does not exceed some safe maximum value for such sideways force. Here we want to join the two straight paths with a continuous curvature curve in between as shown.problem 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we use LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn instead of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn for our parameter for the graph of a function as a vector valued function and 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 the length of the cross product is just the absolute value of the second derivative, and so the curvature formula isLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEieEYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRImZGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSgmc3JhcnI7RidGOUY7Rj5GQEZCRkRGRkZIRmVuL0ZORmZuLUZQNiYtRiM2Ji1GLDYlUSlzaW1wbGlmeUYnRi9GMi1GUDYkLUYjNictSSZtZnJhY0dGJDYoLUYjNilGaW4tRjY2LVEiJ0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xMTExMTExZW1GJ0Zhb0ZicC1GUDYkLUYjNiVGVEZcb0Y5RjktRiw2I1EhRidGXG9GOS1GIzYlLUklbXN1cEdGJDYlLUZQNiQtRiM2KS1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GX3JGaW5GYnAtRmFxNiUtRlA2JC1GIzYlRlRGL0YyRjktRiM2JS1GaHE2JFEiMkYnRjlGL0YyLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YvRjJGOS1GIzYlLUZecDYoLUZocTYkUSIzRidGOUZnci8lLmxpbmV0aGlja25lc3NHRmpxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpzLyUpYmV2ZWxsZWRHRj1GL0YyRlxzRi9GMkZmc0Zoc0ZbdEZddEZXLUYsNiVRKXN5bWJvbGljRidGL0YyRlxvRjlGOUZcb0Y5RjkvJSVvcGVuR1EifGdyRicvJSZjbG9zZUdGZHQtRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GK0ZPRlxvRjk=This is unity for the upper semicircle, as it should be.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Notice that the curvature is zero only when the second derivative equals zero, so to impose that the curvature vanish one only need set the second derivative to zero.a)
By hand one can easily show that the individual formulas of this piecewise function given below agree at the endpoints to make this a continuous function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn. One can also observe from the geometry of the 45 degree arc of the circle that the slopes also agree (negative reciprocal slope to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJ4RidGL0YyRjVGMkY8 is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZFLUkjbW5HRiQ2JVEiMUYnRi9GMkYvRjI= for the tangent line, sides of unit hypotenuse isoceles triangle have length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEiMUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiL0YnRi9GMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkotSSZtc3FydEdGJDYjLUYjNiUtRiw2JVEiMkYnRi9GMkYvRjJGL0Yy), but clearly the curvature of the straight lines is zero but of the unit circle arc it is 1 (why? how did we define curvature for a circle of radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn ?) so the curvature is highly discontinuous. The plots show the continuity of the value and first derivatives at the endpoints. [We need equal units on both axes to make the circle look like a circle!]Edit the rest for part b) below once you find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= to replace 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 and edit the other inputs to adjust to the new plot 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For the circular example, the curvature is a unit step function on the interval between 0 and 1.
b) How to join the two straight lines with continuous curvature across the gap shown in the original plot?Now consider the piecewise function for which LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= is zero for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEmJmxlcTtGJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tSSNtbkdGJDYlUSIwRidGMkY8RjJGPA== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEvJkdyZWF0ZXJFcXVhbDtGJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tSSNtbkdGJDYlUSIxRidGMkY8RjJGPA== but a 5th degree polynomial
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
in between and impose that the function value and slopes agree at both ends, and that the curvature is continous at each end where it should have the value 0 of the straight lines (which is simply 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). The three conditions at the left end for a quadratic function require that it be identically zero (why?) which will make the first three coefficients zero, leaving three conditions at the right end for the remaining 3 coefficients in the polynomial (value 1, slope 1, curvature 0). These are linear equations for the remaining 3 coefficients that Maple easily solves. You can then plot the piecewise curve and curvature as above. Ask bob for help along the way.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 curvature function is complicated.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIlFGJ0YvRjIvJStleGVjdXRhYmxlR0ZFRkFGQUZlbkZBNext write out the 6 conditions on this polynomial separated by commas and use the context menu Solve, Solve (general solution) to get the coefficients which do the job:
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
Then redefine LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn below with those coefficients and edit the plot of the function and its curvature above. The resulting plot of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= should look like the figure at the top of this page. Then plot LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEiUUYnRi9GMkY1RjJGREYyRkRGMkZE. You will see it rise from zero to its first max, then descrease to zero as it curves up from the horizontal and then straightens out to change concavity from down to up at the point of inflection and then curve down to meet the endpoint.
What is the maximum curvature and where does it take place? [Set the derivative to zero.]LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Edit these coefficients which is an example just to show you how to plot these and find the local maxima which occur. For our problem there are two local maxima, due to the "S" shape of the connecting curve.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=