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Appendix 



Define a function G such that 

 dx 



\^L = G[x]-G[x l 



J u[x\ 



where x is the tag's current position in space, x Q is 

 the tag's initial position, and u is the velocity. 



Then 



d c dx dG[x] 



d f dx 

 dx J u [x] 



[x] dx 



From the fundamental theorem of integral calculus 



1 dx 1 dx dG[x] 



u[x] dx u[x ] dx dx 



which reduces to 



dx 



