转子进动定理的扩充和完善

In order to reveal the features of precessional motion of rotors, two theorems on the precessional orbits of rotors are developed. Theorem 1 shows that the area surrounded by an elliptical orbit of rotor precession can directly be obtained in terms of the determinant of matrix constituted by components of rotor precession at the same frequency. Theorem 2 stats that within a same time the precessional vector of a rotor running at constant speed sweeps always a same area, regardless of the origin of the time, that means, the time rate of change of area swept by precessional vector is constant. Furthermore a new operation of inner product of complex vectors is suggested, that is, the inner product of two complex vectors in Euler-form is equal to the product of two magnitudes with cosine of their phase angles. In terms of both theorems and the new operation, the theory of precessional motion of rotors is improved and extended. The result of this paper is an interesting improvement for rotor dynamics.