7.20 * A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates p = R and z = 1ø, where R and à are constants and the z axis is vertically up (and gravity vertically down). Using z as your generalized coordinate, write down the Lagrangian for a bead of mass m threaded on the wire. Find the Lagrange equation and hence the bead's vertical acceleration 2. In the limit that R 0, what is ż? Does this make sense?

Elements Of Electromagnetics
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7.20 classic mechanics 

please provide a solution for the following 

7.20 * A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates p = R and
z = rø, where R and à are constants and the z axis is vertically up (and gravity vertically down). Using
z as your generalized coordinate, write down the Lagrangian for a bead of mass m threaded on the wire.
Find the Lagrange equation and hence the bead's vertical acceleration 2. In the limit that R→ 0, what
is ż? Does this make sense?
Transcribed Image Text:7.20 * A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates p = R and z = rø, where R and à are constants and the z axis is vertically up (and gravity vertically down). Using z as your generalized coordinate, write down the Lagrangian for a bead of mass m threaded on the wire. Find the Lagrange equation and hence the bead's vertical acceleration 2. In the limit that R→ 0, what is ż? Does this make sense?
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