Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



+44 (0)20 7594 1474p.degond Website CV




6M38Huxley BuildingSouth Kensington Campus






BibTex format

author = {Degond, PAA and Frouvelle, A and Merino, Aceituno S and Trescases, A},
doi = {10.1137/17M1135207},
journal = {Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal},
pages = {28--77},
title = {Quaternions in collective dynamics},
url = {},
volume = {16},
year = {2018}

RIS format (EndNote, RefMan)

AB - We introduce a model of multiagent dynamics for self-organized motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbors. The body attitudes are represented through unitary quaternions. We prove the correspondence with the model presented in [P. Degond, A. Frouvelle, and S. Merino-Aceituno, Math. Models Methods Appl. Sci., 27 (2017), pp. 1005--1049], where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual-based model introduced here is based on nematic (rather than polar) alignment. From the individual-based model, the kinetic and macroscopic equations are derived. The benefit of this approach, in contrast to that of the previous one, is twofold: first, it allows for a better understanding of the macroscopic equations obtained and, second, these equations are prone to numerical studies, which is key for applications.
AU - Degond,PAA
AU - Frouvelle,A
AU - Merino,Aceituno S
AU - Trescases,A
DO - 10.1137/17M1135207
EP - 77
PY - 2018///
SN - 1540-3459
SP - 28
TI - Quaternions in collective dynamics
T2 - Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
UR -
UR -
VL - 16
ER -