7Rigid bodies
IA Dynamics and Relativity
7 Rigid bodies
This chapter is somewhat similar to the previous chapter. We again have a
lot of particles and we study their motion. However, instead of having forces
between the individual particles, this time the particles are constrained such
that their relative positions are fixed. This corresponds to a solid object that
cannot deform. We call these rigid bodies.
Definition
(Rigid body)
.
A rigid body is an extended object, consisting of
N
particles that are constrained such that the distance between any pair of
particles, |r
i
− r
j
|, is fixed.
The possible motions of a rigid body are the continuous isometries of Euclidean
space, i.e. translations and rotations. However, as we have previously shown,
pure translations of rigid bodies are uninteresting — they simply correspond to
the center of mass moving under an external force. Hence we will first study
rotations.
Later, we will combine rotational and translational effects and see what
happens.