Simultaneous containment of several polygons : analysis of the contact configurations
Texte intégral
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(48) 3suBthv nlquf3mhf*¦fBqVv;nlf vwBg{fBvÿnlt.
(49) rLt{Cm ~0hV|=ovgnpmg\hVm k$vq1m wBq39vw0hXvrLqVtvqy~3qiksVquf3m{z0nñrvawBrLt{ ²Jm ~3hV|=nLmfBqVf%{x.~Bvÿkz"h |=qVf
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(54) 3sVTthv nlqVf qr .$0ýhXf*IgfBquvH.40 IKJ vawB@q3
(55) ª \|}v;.L0nf vwT|=qVf
(56) 3suBthv nlqVfM=?0 ýdgf°0m 3hjixh}k¦vaq.t{~Btajm {fBv h~3qmÿnlvÿnqufCrquth@m kTm vaxDqXrN7gqU ªÿj|=vmnpmMvaq3m 7hO7 ²-nlx.{f3monlqVf3h\i m ~3hu|}evawB7|=qVf
(57) 3sVTthv nlqVf m ~0hV|=F=P3 2=Q+R}}SRT=GUA@VB D ¯ npmh.|=qVf
(58) 3suBthv nlqVf qXrývwT|=qVx.~ ilvam kTm vax$ ³ MfTqBHL3fT/hrLt{|}quf'3suBthXvÿnqufhumh(|}quf'3suBthXvÿnqufCwB{t/vawB;|ilqm Tt/qrTvawB/q3'ªÿ\|}vm w0h1VgfBqnfTv{tm \|}vÿnquf zhf*°h|}qufBvhV|=v(|}qVf
(59) 3suBthv nlquf°hVmh.|=qVf
(60) 3suBthv nlquf wTt7vwT@nlfva{t nqut qrvawBq3'ªÿ\|}vm w0hgfTqnlfBvatm j|=v nlqVfITBvvawB=nt3qVBfBhtk w3hVgqVfTjm{Md7md2 f0hjnlx d2 f¥B ilv(3m{fBquv. IKJ [ ,(3^].hf*>Z 1_R`1b3c I2J [ . g Ife 3h]ji W 3 XY=;3 2= Q R}\}R?= U TRZL1. 0\ a `dR_. 0\ npmvwTrLt{m ~3hu|} k 3 XY=;3 l= Q R}\}R?= U TR?=@: a WRlZ 16. m 0 I2J [ ,n a `dRM. m 0 IKJ [ . m g Ioe 3^]ji m 3^].hf*>Z 1_R`1b3c npmvwT|=qVfTvhu|}v(m ~3hu|}[ p m {fBqVva7vwT@nf vat nlqutqrhma{v p IqJ [ ,(3\]ji W 0 3 XY= 0 R_. 0h npmvwTrLt{m ~3hu|}7qXrýqufilk qVfT@q
(61) ªÿj|=vb.$0nlf1vawB7fanltqufBx.{fv;, IKJ [ . g Ioe 3^]di W 0 g 3 XY=G0Lrs= g Rl. 0h npmvwTrLt{m ~3hu|}7qXrN.0et}iphv nV =ik.vaqt. g u 0 g 3 XY= 0 rs= g R8= 0 @VW 0 R8= g @VW g R8= 0 rs= g @VW 0 g i npmvwTm {vqrta}iphXvÿnV rLt|}quf'0sVBthXvÿnquf3mqr . 0 hf*v. g nfs, wx0 g 3 XY=G0Lrs= g R?yj=@vWPRz=0ýhXf*/= g ht@vawB1 Çï hXf*{` Çï |=qVx.~3qufB{fBvm/qr =Si npmvwTm {vqrta}iphXvÿnV rLt|}quf'0sVBthXvÿnquf3mqr . 0hf*v. g nf°vawB|}qux.~ilva m kTm vax5qXrF7q3'ªÿj|=vmnlf°vawB7f
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(67) §wT
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(70) {tf0|} hf*Nw np|}wq\m@fTqVv 0qVth²sV{fB{thji/~3qXilk suqVfEhf*Sh%|=qVf
(71) V R~3qiksVquf zevawBCtajm iv|hf
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(74) wx0 g u 0 g [ ou 0 -u g Oa wTta 1A3 a ` 3 a M3^ a 1 hf*ynlf°vawBm ~3j|nLh\iý|{hVm 7qXrývawBt{q
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(78) ;hXtvzO²maTx.xyht n>±{\m7m qVx..|}quf3mon{thv nlqVf0m7h13quBvvawB.|}qufBvhV|=vm ~0hV|}.hf*°jm vh1 i npm wB\m7h fTj|=jmmhtk7hf*@m ²|nl{fBv
(79) |=qVf*nlv nlqVf7qXrB|}quf3|{h1VnvÿkrLqVtehZ {tva qXr Wgz{nlf;hXtavvawB nLm vaf0|}/qr hP qVail ²J|}qufBvhV|=venLm~TtqX@nfCvq7~0hXtvÿnp|} iLht|hum jmrLqVt;vawBta q3'ªÿ\|}vm ývawBt{g|=qVf
(80) V ~3qXilk ² suqVf0m nfyhg~3qiksVquf3h\i"{f'VntaqVfTx.f vequt;vwTt~3qiksVquf3mnlfCht\|}vhXfTsXil§wnpmM~Ttqu~"{tvakgnpm rJh\ipm rLqVt;x.qutvaw3hXfvawBt{ ~3qXilksVquf3mqutrqutvawBt{ fTqVf.|}qufV ~3qilk sVquf3mnlfChfBquf¦|=qVf
(81) V f
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(83) ?v 3|=jm8rLtqVx9vawB/L npm v{f3|=/Q qXr, qVail|}qufBvhV|=vm{zjhXfh\isuqVt nlvawBx9vq$0f* qufBg|=qVfTvhu|}vM|=qVf'0sVTthXvÿnlqVfnñr8nlvM nLm vm/qufB(nlfCvÿnx [#®¯ 9Q¯BiqusA9c_Z{b-«x¬.[#®,°S9I°3iqusA9 rLqVtv9ql_ Z{b-«k¬vwTt1M|}quf
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