Translation mode of a circular boundary
= Translation mode of a circular boundary
{title2=$m=1$}
The first polar sine and cosine harmonics of a circular boundary represent displacements of its centre. A complete translation leaves perimeter and area unchanged, so <line tension> supplies zero stiffness to these modes. The centre of an unconfined domain has no normalizable positional <thermal equilibrium> in an infinite plane; recentering the boundary removes this freedom from a shape spectrum.