Reply to "Comment on "Velocity and Speed Correlations in Hamiltonian Flocks"

TL;DR

This paper responds to comments questioning the presence of rigid body rotations in bird flocks, clarifying concepts and defending the relevance of studying spatial speed correlations in collective animal behavior.

Contribution

It clarifies the definitions of rigid body rotations and rigidity, and defends the importance of analyzing spatial correlations in bird flock dynamics.

Findings

Clarification of rigid body rotation concepts

Justification for studying speed correlations

Defense of previous analytical approaches

Abstract

In their comment on our work (ArXiv:1912.07056v1), Cavagna \textit{et al.} raise several interesting points on the phenomenology of flocks of birds, and conduct additional data analysis to back up their points. In particular, they question the existence of rigid body rotations in flocks of birds. In this reply, we first clarify the notions of rigid body rotations, and of rigidity itself. Then, we justify why we believe that it is legitimate to wonder about their importance when studying the spatial correlations between speeds in flocks of birds.