A railroad track of length L is to be constructed over an uneven terrain by adding...

 

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A railroad track of length L is to be constructed over an uneven terrain by adding or removing dirt (Fig. 1.16). The absolute value of the slope of the track is to be restricted to a value of ri to avoid steep slopes. The absolute value of the rate of change of the slope is to be limited to a value rz to avoid rapid accelerations and decelerations. The absolute value of the second derivative of the slope is to be limited to a value of r3 Terrain (known elevation, g(x)) Track (unknown elevation, h(x)) g(x) (2 b. h(x) L. Figure 1.16 Railroad track on an uneven terrain. to avoid severe jerks. Formulate the problem of finding the elevation of the track to minimize the construction costs as an OC problem. Assume the construction costs to be proportional to the amount of dirt added or removed. The elevation of the track is equal to a and b at x = 0 and x = L, respectively. A railroad track of length L is to be constructed over an uneven terrain by adding or removing dirt (Fig. 1.16). The absolute value of the slope of the track is to be restricted to a value of ri to avoid steep slopes. The absolute value of the rate of change of the slope is to be limited to a value rz to avoid rapid accelerations and decelerations. The absolute value of the second derivative of the slope is to be limited to a value of r3 Terrain (known elevation, g(x)) Track (unknown elevation, h(x)) g(x) (2 b. h(x) L. Figure 1.16 Railroad track on an uneven terrain. to avoid severe jerks. Formulate the problem of finding the elevation of the track to minimize the construction costs as an OC problem. Assume the construction costs to be proportional to the amount of dirt added or removed. The elevation of the track is equal to a and b at x = 0 and x = L, respectively.

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