nLab rigid body dynamics




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



The mechanics of rigid bodies in Cartesian space.

Up to the dynamics of the center of mass?, this is the special case of Hamiltonian dynamics on Lie groups for the case of the special orthogonal group SO(n)SO(n).

Often this is considered (only) for n=3n = 3, which is the case pertaining to rigid bodies in observable nature, hence using SO(3).


A general introduction is in section 1.1d of

A discussion from the more general perspective of Hamiltonian dynamics on Lie groups is in section 4.4 of

A discussion of rigid body dynamics as a special case of the general Euler-Arnold equation is at

References from the point of view of Geometric Algebra include

  • David Hestenes, Rotational dynamics with geometric algebra (web)

  • Terje Vold, An introduction to geometric algebra with an application to rigid body mechanics (pdf)

Discussion of (geometric) quantization of rigid bodies is in

  • M. Modugno, C. Prieto, R. Vitolo, Geometric aspects of the quantization of a rigid body, in B. Kruglikov, V. Lychagin, E. Straume, Differential Equations – Geometry, Symmetries and Integrability, Proceedings of the 2008 Abel Symposium, Springer, 275-285. (pdf)

Last revised on March 22, 2019 at 13:47:36. See the history of this page for a list of all contributions to it.