{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T00:23:30Z","timestamp":1780619010204,"version":"3.54.1"},"reference-count":32,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T00:00:00Z","timestamp":1735776000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>Professor Richard Klein and his students built a bicycle with a rather interesting feature: no one was able to ride it. A prize was offered. Hundreds of students and cycling enthusiasts attempted it. Years passed, and the prize money grew. Klein\u2019s rear-steered bicycle became a canonical example of how non-minimum phase systems can be difficult and sometimes nearly impossible to control. It has been lauded as a particularly effective educational example in which students can <jats:italic>experience<\/jats:italic> the loss of controllability in a seemingly simple, albeit unorthodox bicycle. The primary result of the work reported here is a demonstration that it is possible for a human of modest athletic ability to ride Klein\u2019s unridable bicycle, to keep it balanced, and to control its direction of travel. There is a secret to riding Klein\u2019s rear-steer bicycle. The secret is revealed through an exploration of the dynamics and control of the bike that contains three elements: (1) modeling the physics of the actively steered bicycle as an inverted pendulum riding atop a carriage; (2) recognizing that the steer kinematics leads to competing physical mechanisms which an aspiring rider might exploit; and (3) examining limitations of controllability and stabilizability of the system from a state space perspective. From this vantage point, one can devise a novel strategy, based on a component of lateral acceleration that dominates at low speed, for riding the so-called \u201cunridable\u201d bike and solving Klein\u2019s puzzle. The work adds a new chapter on the dynamics and control of the rear-steered bicycle, a problem of academic interest.<\/jats:p>","DOI":"10.1371\/journal.pone.0315769","type":"journal-article","created":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T19:03:52Z","timestamp":1735844632000},"page":"e0315769","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["The right way to ride the wrong bike: An exploration of Klein\u2019s \u2018unridable\u2019 bicycle"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6704-1153","authenticated-orcid":true,"given":"B. 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