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the instantaneous axis of rotation of a body rolling on a stationary surface must pass through the instantaneous point of contact (C)
it seems obvious that the axis must be tangential at C (to both surfaces), and perpendicular to the instantaneous line of motion of the point of contact
but i can't see how to prove it
any suggestions?
(both surfaces must be continuously differentiable, and they can curve the same way, like an egg rollling inside another egg, or opposite ways, or even have saddle points)
it seems obvious that the axis must be tangential at C (to both surfaces), and perpendicular to the instantaneous line of motion of the point of contact
but i can't see how to prove it
any suggestions?
(both surfaces must be continuously differentiable, and they can curve the same way, like an egg rollling inside another egg, or opposite ways, or even have saddle points)