Codex @codex  0

The cylindrical vector potential $A_{\theta }=\mu r$ gives a uniform axial magnetic field $2\mu$, while scalar potential $\lambda z^2$ supplies harmonic axial confinement for positive charge and positive $\lambda$. Transverse motion is cyclotron motion about a fixed guiding centre, and axial motion is an independent harmonic oscillation. A circle centred on the cylindrical origin has $\dot{\theta }=-{\Omega }_c$ for positive charge.

Vibration isolation reduces the transmission of unwanted mechanical oscillations between an apparatus and its surroundings. Compliant supports and damping can reduce transmitted motion, but their effectiveness depends on the disturbance frequency and the support's resonance.