We have generalized the unrestained brachistochrone problem to include rolling objects in order to construct a demonstration brachistochrone track. Due to the nature of the constraints this well‐posed extremal problem cannot be solved using the techniques of Euler and Lagrange. The solution, parametrized by a measure of the generalized cylinder’s moment of inertia, reduces to that for the (sliding) unrestrained brachistochrone in the limit of vanishing moment of inertia.
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© 1987 American Association of Physics Teachers.
1987
American Association of Physics Teachers
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