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2. Brachistochrone in polar coordinates. Assume that a planet of viscous gas permits for the speed v = c r where r is the distance from the center. Describe the brachistochrone: the fastest path between the given points (R, 0) and (R, \theta ) in polar coordinates (r, \theta ). (We assume that the path is a curve in the plane that passes through points of origin and destination, and the center of the planet.) Write the distance ds in polar coordinates, formulate Lagrangian, find first integral. Solve in quadratures.