Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review

  title={Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review},
  author={Jacob P. Meijaard and Jim Papadopoulos and Andy Ruina and Arend L. Schwab},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  pages={1955 - 1982}
We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetric ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edge rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrary. This conservative non-holonomic system has a seven-dimensional accessible configuration space and three velocity degrees of freedom parametrized… 

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