An improved model of orbital dynamics

The radius vector of spacecraft can be decomposed into the product of the mold and the unit vector. Using this property, the traditional orbital dynamics equation can be transformed into two equations which describe the mold's and direction's motions separately. The mold's equation can be converted to a linear equation without singularity by introducing the inverse of the mold; and using the variation of constants method, the linear equation can be reduced to one-order. As for the direction's equation, the quaternion description is suitable. This equation can be completely solved. Through the above handling methods, we obtain a new orbital dynamic model which contains seven equations. In the sense of the virtual time, the angular velocity of the spacecraft depends only on the normal force. This new orbital model is applicable to any form of thrust or perturbation. At the same time, we get seven new stable variables which completely equivalent to the kepler elements. And the transforming relationship has been established. In the end of this article, we verify the accuracy and applicability of the new model in the cases of constant and variable thrusts.