In Example 4.8 we analyzed the case of a bead on a rotating parabolic wire. The energy of the bead was not conserved, but the Hamiltonian was:

There is an equilibrium point at \(r=0\) which is unstable if \(\omega>\omega_{0} \equiv \sqrt{2 g} \alpha\), neutrally stable if \(\omega=\omega_{0}\), and stable if \(\omega

Data from Example 4.8

Transcribed Image Text:

where 1 H=m(1+4a) + Ueff = constant, 1 Ueff = m (2ga - w). 2