For interacting particles, the equation of motion becomes d d t [ ( 1 + 1 2 v 1 2 c 2 ) m 1 v 1 + q 1 c A ( r 1 ) ] = − − ∇ ∇ q 1 q 2 r + ∇ ∇ [ q 1 q 2 r 1 2 c 2 v 1 ⋅ ⋅ [ 1 + r ^ ^ r ^ ^ ] ⋅ ⋅ v 2 ] d p 1 d t = q 1 q 2 r 2 r ^ ^ + q 1 q 2 r 2 1 2 c 2 { v 1 ( r ^ ^ ⋅ ⋅ v 2 ) + v 2 ( r ^ ^ ⋅ ⋅ v 1 ) − − r ^ ^ [ v 1 ⋅ ⋅ ( 1 + 3 r ^ ^ r ^ ^ ) ⋅ ⋅ v 2 ] } p 1 = ( 1 + 1 2 v 1 2 c 2 ) m 1 v 1 + q 1 c A ( r 1 ) A ( r 1 ) = q 2 2 c 1 r [ 1 + r ^ ^ r ^ ^ ] ⋅ ⋅ v 2 r = r 1 − − r 2