Abstract:

A bicycle system is a complicated one with non-complete constraints，which can be solved by the

Euler-Lagrange equation according to least action principle. The approximate calculation is solved by using the

difference instead of the differential and methods to correct the truncation error. Using MATLAB，as long as Lagrangian function of any system with finite degrees of freedom and the constraints are provided，the approximate solution

can be found. And this simple method can be applied to the approximate calculation of the bicycle system to

analyze the motion and stability of the bicycle.

Key words: analytical mechanics, non-complete system, stability of the bicycle