A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

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