PX155 - E10 - systems of particles III

PX155 - B1 - systems of particles I
PX155 - E6 - system of particles II

rigid body of $N$ particles
consider the angular momentum of a single particle:

\vec{L} = {\vec{r}}_{i} \times {\vec{p}}_{i} = {\vec{r}}_{i} \times (m_{i} {\vec{v}}_{i}) = m_{i} {\vec{r}}_{i} (\vec{ω} {\vec{r}}_{i})

Using vector triple product: