Cylinder Rolling on Another Rolling Cylinder
نویسندگان
چکیده
This problem was suggested by Bradley Klee. For the related case of one cylinder rolling inside another, see [1]. When one cylinder is directly above the other, we define the line of contact of the lower cylinder, 1, with the horizontal plane to be the z-axis, at x = y = 0. Then, the condition of rolling without slipping for the lower cylinder is that when it has rolled (positive) distance x1, the initial line of contact has rotated through angle φ1 = x1/r1, clockwise with respect to the vertical, as shown in the figure below. This rolling constraint can be written as
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