A bead slides without friction down a wire that has a shape y = f(x). (a) Prove that the EOM is (1 + f′2)¨x + f′f” ˙x2 + gf′ = 0 (where f′ =df/dx , f” = d2f/dx2 ). (b) Since the Hamiltonian is constant in this problem, it always equals its value at t = 0. Use this fact to solve x˙(t).
A bead slides without friction down a wire that has a shape y = f(x). (a) Prove that the EOM is (1 + f′2)¨x + f′f” ˙x2 + gf′ = 0 (where f′ =df/dx , f” = d2f/dx2 ). (b) Since the Hamiltonian is constant in this problem, it always equals its value at t = 0. Use this fact to solve x˙(t).
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A bead slides without friction down a wire that has a shape y = f(x).
(a) Prove that the EOM is
(1 + f′2)¨x + f′f” ˙x2 + gf′ = 0
(where f′ =df/dx , f” = d2f/dx2 ).
(b) Since the Hamiltonian is constant in this problem, it always equals its
value at t = 0. Use this fact to solve x˙(t).
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