Consider a rightcircular cylinder oriented in the z-direction and with a diamete

Question

Consider a rightcircular cylinder oriented in the z-direction and with a diameterof d = 2 m. Find the equation of a curve on the surface of thiscylinder (i.e., a geodesic) linking the points a and b, where inCartesian coordinates (x,y,z) we have a = (-1, 0, 0) and b = (1, 0,1), such that the length of the curve/line is a minimum. That is,you need to find the curve specified by y(x) and z(x), if x ischosen as the independent variable. You might start byparameterizing the curve in terms of another variable (e.g., theazimuthal or polar angle, ) –x(), y(),z()). Show your results both ways. Alsofind thelength of the curveand sketch the curve on a diagram. Explicitly use Euler’s equations with a constraintto carry this task out. Show all work and manipulations in order to getcredit.

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