A rectangle with coordinate system with axes x,y,z is rotating relative to an inertial frame with constant angular velocity w about the z-axis. A particle of mass m moves under a force whose potential is V(x,y,z). Set up the Lagrange equations of motion in the coordinate system x,y,z. Show that their equations are the same as those in a fixed coordinate system acted on by the force -grad(V) and a force derivable from a velocity dependent potential U. Find U.
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