Classical Mechanics (Kibble & Berkshire) · Problem 14.2

The general theory of small oscillations — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · hamiltonian-helix

Problem

A smooth wire has the form of the helix

x = a\cos\theta

y = a\sin\theta

z = b\theta

, where

\theta

is a real parameter, and

a

b

are positive constants. The wire is fixed with the axis

Oz

pointing vertically upwards. A particle

P

of mass

m

can slide freely on the wire. Taking

\theta

as generalised coordinate, find the Hamiltonian and obtain Hamilton's equations for this system.