The self-stabilising dynamics of bicycles

Details The self-stabilising dynamics of bicycles The self-stabilising dynamics of bicycles

2010-09-28

arxiv.org/abs/1009.5574v3

Physics

Classical Physics

This paper has been withdrawn since it needs extension to how gyroscopic effects impact on the transition back from stable to

Scientific paper

We analyse the classical problem of the stability of bicycles when moving quickly and upright. Developing a lean causes the front wheel to turn thereby setting the bicycle instantaneously into circular motion. The centripetal force associated with the lean-dependent turning circle gives a restoring torque which corrects the lean. The force also helps self-steer the front wheel, ensuring the bicycle continues in an essentially straight path. We give the frequency of lean oscillations about the vertical executed during riding. As in the literature, we discuss the neglect of gyroscopic effects, which experiment suggests are negligible.

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