The total linear momentum and angular momentum of the system are p = d d t ( ∑ ∑ i = 1 n m i ( r i − − R ) ) + ( ∑ ∑ i = 1 n m i ) v , and L = ∑ ∑ i = 1 n m i ( r i − − R ) × × d d t ( r i − − R ) + ( ∑ ∑ i = 1 n m i ) [ R × × d d t ( r i − − R ) + ( r i − − R ) × × v ] + ( ∑ ∑ i = 1 n m i ) R × × v