In this paper, the third order Lagrange equation is obtained, by which can be obtained motion equation of a body. This equation contains third order rate of change of generalized coordinates and the rate of change of force. In addition, the third order Lagrange equation and the fraditional Lagrange equation are used to solve the same problem of the motion of a body, and their results are discussed. Finally, it is pointed out that the third order Lagrange equation provides a method of obtaining equation of motion which is different from that of the traditional Lagrange equation.
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