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Home/ Questions/Q 565101
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Editorial Team
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Editorial Team
Asked: May 13, 20262026-05-13T12:50:12+00:00 2026-05-13T12:50:12+00:00

Assume you have a flat plane, with a bicycle resting on it. As the

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Assume you have a flat plane, with a bicycle resting on it. As the bicycle enters a turn, it leans into the turn with angle theta. At the same time, the bike frame points in the same direction as the bike velocity.

Thus, given the bike velocity vector v (assumed to be in the XZ plane) and the lean angle theta, how can you find the rotation matrix for the bike?

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  1. Editorial Team
    Editorial Team
    2026-05-13T12:50:12+00:00Added an answer on May 13, 2026 at 12:50 pm

    Use a quaternion. Axis is bike velocity and ‘lean into turn’ is axis angle.
    Then convert to rotation matrix

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