Particles and Rigid Bodies

The simplest dynamical systems are particles. The particle is idealized as a “point – mass,” meaning that it takes up no space even though it has nonzero mass. The position vector of a particle in a Cartesian frame can be characterized in terms of its three Cartesian coordinates—for example, x, y, and z. Particles have velocity and acceleration but they do not have angular velocity or angular acceleration. Introducing three unit vectors, i, j, and k, which are regarded as fixed in a Cartesian frame F, one may write the position vector of a particle Q relative to a point O fixed in F as

Pq = ХЇ + yj + zk (2.1)

The velocity of Q in F can then be written as a time derivative of the position vector in which one regards the unit vectors as fixed (i. e., having zero time derivatives) in F, so that

vq = ХЇ + yj + Zk (2.2)

Finally, the acceleration of Q in F is given by

aQ = ХЇ + yj + Zk (2.3)