Kinematics of the Rolling Sphere and Quantum Spin∗
نویسندگان
چکیده
We consider the kinematics and control of a sphere rolling of a curved surface and analyze its rotation by mapping the system to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. This mapping is useful in understanding the role of the geometrical phase and generalizes the kinematic control problem of a ball rolling on a plane.
منابع مشابه
The rolling sphere, the quantum spin and a simple view of the Landau-Zener problem
We consider the problem of a sphere rolling on a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin precession. As an interesting example we show that the Landau-Zener problem corresponds to the rolling of a sphere on a Cornu spiral, and deriv...
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