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Starting from normalized generators equations of rotor motion with respect to the center of inertia of power systems, post-fault power system dynamic is analogized as a motion of a particle with 1.0 mass in an n-dimensional Euclidean space. A rotational coordinate axis is defined for the moving particle. Transient stability of a multi-machine power system is transformed into a simple one-dimensional motion of particle on the axis. Based upon the above new idea, a new concept transient energy function (NCTEF) is proposed for transient stability assessment of power systems. Case studies on the 10-generator New England power system verified the rationality of NCTEF.