Lecture Notes #8 - Dimensional Analysis, Similarity Solutions, Perturbation Theory.pdf

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Xki{|yk ±Pptkuzpvugs Mugs zpz ˙˳_ptpsgyp{ _vs|{pvuzYvz{glg Zgqgōŧ g jpPkwgy{tku{ vl Ykiogupigs QunpukkypunYiSpss aup}kyzp{ tvz{glg.ugqgōŧ g jp˝˷tinpss.igYQOT ²³´/³´µ
Pptkuzpvu\yptgy jptkuzpvuz:Ygzz → YXkun{o → X`ptk → `Q gtwsk:[`ktwkyg{|yk] = X / `[Qski{ypi Oogynk] = Y´/¶X·/¶/ `[`okytgs ivuj|i{p}p{ ] = ´ / X`
Zvu-jptkuzpvugs u|thkyz ˙˳ \o zpizMzz|tw{pvuz:´.Mss jptkuzpvugs }gypghskz igu hk uvu-jptkuzpvugsp kj.¶.\o zpiz pz pyykzwki{p}k vl zigskz guj |up{z.
Pptkuzpvugs Yg{yp ^gur vl tg{yp = zp k vl {ok sgynkz{ zx|gyk z|htg{yp {og{ ogz g uvu kyv jk{kytpugu{{kssz ov~ tgu lk~ky }gypghskz ~pss vii|y ~oku g l|ui{pvu pz k wykzzkj puuvu-jptkuzpvugs }gypghskz.^gur = ·
N|irpunogt’z \p `okvyktMzz|tk {og{ ~k gyk np}ku g wyvwky wo zpigs l|ui{pvu ~p{o[n}gypghskz:guj gss }gypghskz igu hk ivu}ky{kj lyvt vuk |up{ z z{kt {v guv{oky h Nypjntgu’zkx|g{pvu:~okykF’z gyk wyptgy jptkuzpvuz. `oku, {ok vypnpugs l|ui{pvu igu hk k wykzzkj gz~okykZm = [n - _r~p{o_rhkpun {ok ygur vl {ok jptkuzpvugs tg{yp ˢ(Zv. vl ukikzzgy wyptgy jptkuzpvuzˣ).
Tv~ {v ōŧuj g zk{ vl ɛɵ uvu-jptkuzpvugs }gypghskz?Rvytgs tk{ovj ˢ(N|irpunogt, ´¸´¹ˣ):´.Oovvzk_rykwkg{pun }gypghskz lyvt {okx}gypghskz ˢ(spukgys pujkwkujku{ˣ)g.Xpukgy pujwkujku{x’zz|htg{yp vl {okpyjptkuzpvugs k wvuku{z t|z{ og}kuvu- kyv jk{kytpugu{.h.^kwkg{pun }gypghskz ~pss gwwkgy puLQYlYluvu-jptkuzpvugs u|thkyz.

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