Arjan vat, dez SCHAFT Res'Fted ] July 1911 tum~ tern 141hoot a I¢'ra~ I¢~m) H*.~ to~trt t31~ laknoOw-'.to o In [he context o| r,onllne~r Hamiltonhn sys-wi~ul ~te~ta] fo~ the stpdy of.sT~ trh= is a ~ imp,:rtmtt ,rod eisbo~ted issue (cf. [1,2 D. "i'he main reason for th¢ unport~ace of ~mmetti~ tt that they ~ ~uiva]~t to the ~-ist~ of ~t~ Imps. Le. functions of the state which ~ unaltered in tlme(this is ~xu-alP1 ~'Iod Nog-d~n'~ that--). ~ ~nt~'~t of paper is to z-~enc~cadite th= om~.xpt of syl~lletriss and co~a~a~icaa laws to ~-,.o~ which ~x~ not "~olated from the ~t~de ~.r]d. ~ozely xpeak2n8 ~tcm.s ~dth ir~ ~d ¢~T:~as. The s~tuafioa mpl~e~ by the foUa,v~g ~mple example. Con~der a particle ia IR ~ with mass m in a Iolentlal tXe.2d ~, m~ also ~bjo~t to ~ ~mal f~ F. Le inlmt-output form the u/zttm it given by y,=q¢ (yis theou pu ). Suppose the ¢~T~dons rn~, ffi OF//E q, ~ invzri.m t ~dcr z~LIt~ ~d ~ et-~c~ (th~ is ¢qldga-l~t ~ ~ ot L:~t~ 2 --V invariant). Then Imow that f~ F=O, thz ~p~hr mom~t~ ~round the el-axls is preserved. L~ O_L/= 0 dt " w~"thl:=(q×~l~'ei)"
H~ev~. for a nonzero ~ternal force we obtain