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Single-Particle Electrodynamics - Assassination Science

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+ 3 4 r s(n d·σ)(n s· ˙v) ˙vרv + 9 4 r s(n d·σ)(n s·¨v)n d רv<br />

+ 3 4 r s(n d·σ)(n s·... v)n d × ˙v + 27<br />

4 r s(n d· ˙σ)(n s· ˙v)n d רv<br />

+ 9 2 r s(n d· ˙σ)(n s·¨v)n d × ˙v + 27<br />

4 r s(n d· ¨σ)(n s· ˙v)n d × ˙v<br />

− 21 8 r s(n s· ˙v)( ˙v·σ)n d רv − 21<br />

4 r s(n s· ˙v)( ˙v· ˙σ)n d × ˙v<br />

− 27 8 r s(n s· ˙v)(¨v·σ)n d × ˙v − 2r s (n s·¨v)( ˙v·σ)n d × ˙v<br />

+ 9 2 r s ˙v 2 (n d·σ)(n s· ˙v)n d × ˙v + 45 4 r s(n d· ˙v)(n d·σ)(n s· ˙v)n d רv<br />

+ 8r s (n d· ˙v)(n d·σ)(n s·¨v)n d × ˙v + 45<br />

2 r s(n d· ˙v)(n d· ˙σ)(n s· ˙v)n d × ˙v<br />

− 33 4 r s(n d· ˙v)(n s· ˙v)( ˙v·σ)n d × ˙v<br />

+ 189<br />

8 r s(n d· ˙v) 2 (n d·σ)(n s· ˙v)n d × ˙v<br />

+ 51<br />

4 r s(n d·¨v)(n d·σ)(n s· ˙v)n d × ˙v + 3 4 r−1 d r2 s (n s· ˙v) 2 n d × ¨σ<br />

+ 9 8 r−1 d<br />

+ 3 4 r−1 d<br />

+ 9 4 r−1 d<br />

+ 3 4 r−1 d<br />

r2 s (n s· ˙v) 2 ˙v× ˙σ + 3 4 r−1r2<br />

s (n s· ˙v) 2¨v×σ<br />

d<br />

r2 s (n d· ˙v)(n s· ˙v) 2 n d × ˙σ + 9 8 r−1r2<br />

s (n d· ˙v)(n s· ˙v) 2 ˙v×σ<br />

r2 s (n d·σ)(n s· ˙v) 2 n d רv + 9 2 r−1r2<br />

s (n d· ˙σ)(n s· ˙v) 2 n d × ˙v<br />

r2 s (n s· ˙v)(n s·¨v)n d × ˙σ + 3 4 r−1r2<br />

s (n s· ˙v)(n s·¨v) ˙v×σ<br />

− 15 8 r−1 d r2 s (n s· ˙v) 2 ( ˙v·σ)n d × ˙v<br />

+ 63<br />

8 r−1 d<br />

+ 9 4 r−1 d<br />

r2 s (n d· ˙v)(n d·σ)(n s· ˙v) 2 n d × ˙v<br />

r2 s (n d·σ)(n s· ˙v)(n s·¨v)n d × ˙v + 1 8 r−2r3<br />

s (n s· ˙v) 3 n d × ˙σ<br />

+ 1 8 r−2 d r3 s (n s· ˙v) 3 ˙v×σ + 3 8 r−2 d r3 s (n d·σ)(n s· ˙v) 3 n d × ˙v + O(ε 2 ),<br />

d<br />

d<br />

d<br />

d<br />

492

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