3. A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylin- drical polar coordinates (p, ø, z) satisfying z The z axis points vertically up and gravity vertically down. co and p = R, with c and R constants (a) as a function of and its conjugate momentumpo. (b) Using as your generalized coordinate, write down the Hamiltonian H Write down the Hamilton's equations and solve for ø and hence z.
3. A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylin- drical polar coordinates (p, ø, z) satisfying z The z axis points vertically up and gravity vertically down. co and p = R, with c and R constants (a) as a function of and its conjugate momentumpo. (b) Using as your generalized coordinate, write down the Hamiltonian H Write down the Hamilton's equations and solve for ø and hence z.
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Transcribed Image Text:3. A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylin-
drical polar coordinates (p, ø, z) satisfying z
The z axis points vertically up and gravity vertically down.
co and p = R, with c and R constants
(a)
as a function of and its conjugate momentumpo.
(b)
Using as your generalized coordinate, write down the Hamiltonian H
Write down the Hamilton's equations and solve for ø and hence z.
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