13.5 ** A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylindrical polar coordinates (p, p, z) satisfying z = co and p = R, with c and R constants. The z axis points vertically up and gravity vertically down. Using o as your generalized coordinate, write down the kinetic and potential energies, and hence the Hamiltonian H as a function of o and its conjugate momentum p. Write down Hamilton's equations and solve for o and hence 2. Explain your result in terms of Newtonian mechanics and discuss the special case that R=0.
13.5 ** A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylindrical polar coordinates (p, p, z) satisfying z = co and p = R, with c and R constants. The z axis points vertically up and gravity vertically down. Using o as your generalized coordinate, write down the kinetic and potential energies, and hence the Hamiltonian H as a function of o and its conjugate momentum p. Write down Hamilton's equations and solve for o and hence 2. Explain your result in terms of Newtonian mechanics and discuss the special case that R=0.
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13.5
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Transcribed Image Text:13.5 ** A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylindrical polar
coordinates (p, ø, z) satisfying z = co and p = R, with c and R constants. The z axis points vertically
up and gravity vertically down. Using o as your generalized coordinate, write down the kinetic and
potential energies, and hence the Hamiltonian H as a function of ø and its conjugate momentum p.
Write down Hamilton's equations and solve for o and hence z. Explain your result in terms of Newtonian
mechanics and discuss the special case that R =0.
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