nLab rigid body dynamics

Idea

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 $SO(n)$.

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

Related concepts

• non-relativistic particle

• Hamiltonian dynamics on Lie groups

  • rigid body dynamics

    • angular velocity

    • angular momentum

    • moment of inertia

• solid state physics

References

A general introduction is in section 1.1d of

• Theodore Frankel, The Geometry of Physics - An Introduction

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

• Ralph Abraham, Jerrold Marsden, Foundations of Mechanics

• Vladimir Arnol'd, Mathematical methods of classical mechanics, Springer 1989 (section 28)

• Landau-Lifschitz, vol.1, Mechanics

• R. Abraham, J. Marsden: The Foundations of Mechanics, Benjamin Press, 1967, Addison-Wesley, 1978; large pdf 86 Mb free at CaltechAuthors

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

• Terence Tao, The Euler-Arnold equation (web)

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)