Burst oscillations in the accelerating bicycle

David J.N. Limebeer, Amrit Sharma

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The purpose of this paper is to study the dynamics of the accelerating bicycle. It is shown that time-scale separation can be used to study the oscillatory characteristics of the accelerating machine using time-invariant models. These models are used to explain practically observed wobble-mode bursting oscillations that are associated most frequently with down-hill riding. If the vehicle is cornering under constant acceleration, at a fixed roll angle, it is shown that for low values of acceleration (and braking), it follows closely a logarithmic spiral shaped trajectory. The studies presented are facilitated by a novel adaptive control scheme that centers the machine's trajectory on any arbitrary point in the ground plane. The influences of cambered road surfaces are also investigated. The bicycle model employed is an extension of that originally developed by Whipple, and comprises two road wheels and two laterally-symmetric frame assemblies that are free to rotate relative to each other along an inclined steering axis. For the most part, the front frame is treated as being flexible and the bicycle is fitted with force generating road tires, rather than classical nonholonomic rolling constraints. This research provides the ground work required for generating more complex dynamic models for high-performance motorcycle studies.

Original languageEnglish
Article number061012
JournalJournal of Applied Mechanics, Transactions ASME
Issue number6
Publication statusPublished - 2010
Externally publishedYes


  • bicycle dynamics
  • bursting phenomena
  • cambered roads
  • d'Alembert's principle
  • multibody mechanics
  • stability
  • time-varying linear systems

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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