Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://lib.sinp.msu.ru/static/tutorials/152_2_Cosm_Lab1.pdf
Äàòà èçìåíåíèÿ: Tue Oct 16 07:15:01 2012
Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 22:23:50 2016
Êîäèðîâêà:
E:;HJ:LHJG:YJ:;HL:
DHKFBQ?KDH?BAEMQ?GB?G:MJH
<\_^_gb_ Dhkfbq_kdb_ emqb wlh ihlhdb Zlhfguo y^_j \ukhdbo wg_j]bc ijboh^ysbo gZ A_fex ba ijhklhjh\ 8


EZevg_crb_ hiulu ih bamq_gbx aZ\bkbfhklb bgl_gkb\ghklb baemq_gby hl \ukhlu ihdZaZeb qlh bf__lky fZdkbfmf bgl_gkb\ghklb dhkfbq_kdbo qZklbp gZ \ukhl_ df gZ^ mjh\g_f fhjy GZ [hevrbo \ukhlZo bgl_gkb\ghklv dhkfbq_kdbo emq_c g_kdhevdh mf_gvrZ_lky Z aZl_f gZqbgZy k \ukhlu dfklZgh\blkyihklhygghc Wdki_jbf_glu\dhkfbq_kdboemqZoiha\hebebk^_eZlvjy^ ijbgpbibZevguo^eynbabdbfbdjhfbjZhldjulbc < ]h^m :g^_jkhg hldjue \ dhkfbq_kdbo emqZo ihabljhg < ]h^m :g^_jkhghf b G_^^_jf_c_jhf [ueb hldjulu fxhgu b mdZaZglbi bojZkiZ^Z<]h^mhldjueb f_ahgu < ]h^m \ dhkfbq_kdbo emqZo mklZgh\beb gZebqb_ Df_ahgh\ Z lZd`_ b ly`_euog_cljZevguoqZklbp]bi_jhgh\ D\Zglh\Zy oZjZdl_jbklbdZ kljZgghklv ihy\beZkv \ hiulZo k dhkfbq_kdbfb emqZfb Wdki_jbf_glu \ dhkfbq_kdbo emqZo ihklZ\beb \hijhk h khojZg_gbb q_lghklb h[gZjm`beb ijhp_kku fgh`_kl\_gghc ]_g_jZpbb qZklbp \ gmdehgguo \aZbfh^_ckl\byo iha\hebeb hij_^_eblv \_ebqbgm wnn_dlb\gh]h k_q_gby \aZbfh^_ckl\bygmdehgh\\ukhdhcwg_j]bb Ihy\e_gb_ dhkfbq_kdbo jZd_l b kimlgbdh\ ijb\_eh d gh\uf hldjulbyf h[gZjm`_gbx jZ^bZpbhgguo ihykh\ A_feb ] KG<_jgh\ b :?Qm^Zdh\ b g_aZ\bkbfh hl gbo \ lhf `_ ]h^m ± 9


y\e_gby k\yaZggu_ k \aZbfh^_ckl\b_f dhkfbq_kdbo emq_c k dhkfbq_kdbfb h[t_dlZfb ieZg_lZfb bo Zlfhkn_jhc b fZ]gblgufbiheyfb ijhp_kku jh`^_gby dhkfbq_kdbo emq_c b bo mkdhj_gby \ dhkfbq_kdhfijhkljZgkl\_ I_j\bqgh_dhkfbq_kdh_baemq_gb_ DZdm`_mihfbgZehkvdhkfbq_kdb_emqbij_^klZ\eyxlkh[hc ihlhdby^_jZlhfh\\hkgh\ghfijhlhgh\jh`^_gguobmkdhj_gguo \ h[t_dlZo dhkfbq_kdh]h ijhkljZgkl\Z Bgl_gkb\ghklv dhkfbq_kdh]h baemq_gby \ i_jbh^ fbgbfmfZ kheg_qghc Zdlb\ghklbkhklZ\ey_l-akf-2k-1 kj-1. Wg_j]bydhkfbq_kdboqZklbp aZdexq_gZ \ rbjhdhf ^bZiZahg_ 9 hl ^h 20 w< 10


KjZ\g_gb_ jZkijhkljZg_gghklb we_f_glh\ \ dhkfbq_kdbo emqZo b \h
JbkObfbq_kdbckhklZ\dhkfbq_kdboemq_c±=ZeZdlbdZ± dhkfbq_kdb_emqbghjfbjh\Zghihkh^_j`Zgbx\h^hjh^Z

Dhebq_kl\h we_dljhgh\ \ i_j\bqghf dhkfbq_kdhf baemq_gbb \ jZaf_gvr_q_fijhlhgh\

11


LZ[ebpZ1 Obfbq_kdbckhklZ\i_j\bqgh]hdhkfbq_kdh]hbaemq_gby =jmiiZy^_j P L M H VH Bgl_gkb\ghklvf-2k-1kj 1300±100 94±4 2,0±0,3 6,7±0,3 2,0±0,3 0,5±0,2

Z 1 2 3 -5 6 -9 10 20

-1

Bkke_^h\Zgby ijh\_^_ggu_ \ ihke_^gb_ ]h^u gZ kimlgbdZo b gZ Emg_ ihdZaZeb qlh obfbq_kdbc khklZ\ i_j\bqgh]h dhkfbq_kdh]h baemq_gby hq_gv keZ[h f_gy_lky k wg_j]b_c ^hey y^_j ]jmiiu / b y^_j k aZjy^hf = mf_gvrZ_lky k jhklhf wg_j]bb ijb wg_j]byoihjy^dZg_kdhevdbo=w 12

(1 )


]^_ ^hwg_j]bb 106=w<
JbkWdki_jbf_glZevgucwg_j]_lbq_kdbcki_dljIDB\ ^bnn_j_gpbZevghcnhjf_\rbjhdhfbgl_j\Ze_wg_j]bcbgl_gkb\ghklv 2 ,5 mfgh`_gZgZE0 )

KZfu_ \ukhdb_ aZj_]bkljbjh\Zggu_ agZq_gby wg_j]bb qZklbp ^hklb]Zxl 1020 -1021 w< J_]bkljZpby qZklbp h[eZ^Zxsbo klhev \ukhdhc wg_j]b_c \uau\Z_l ih\ur_gguc bgl_j_k ihkdhevdm kms_kl\mxl ^hdZaZl_evkl\Z \ ihevam lh]h qlh \ dhkfbq_kdbo emqZo g_^he`gh[ulvqZklbplZdbo\ukhdbowg_j]bc >_eh \ lhf qlh gZrZ 13


wg_j]b_c !20 w< Ihwlhfm \hijhk h kms_kl\h\Zgbb j_ebdlh\h]h h[j_aZgbyhklZ_lkyhldjuluf Bklhqgbdb dhkfbq_kdbo emq_c HdhgqZl_evghc l_hjbb ijhbkoh`^_gby dhkfbq_kdbo emq_c \ gZklhys__ \j_fy ihdZ _s_ g_l Ex[Zy fh^_ev ij_l_g^mxsZy gZ wlm jhev ^he`gZ h[tykgblv hkgh\gu_ mklZgh\e_ggu_ wdki_jbf_glZevgu_ oZjZdl_jbklbdb i_j\bqguodhkfbq_kdboemq_cZbf_ggh nhjfmwg_j]_lbq_kdh]hki_dljZdhkfbq_kdboemq_c obfbq_kdbckhklZ\dhkfbq_kdboemq_c ihegmxwg_j]bxdhkfbq_kdboemq_c ijZdlbq_kdb ihklhyggmx \h \j_f_gb bgl_gkb\ghklv dhkfbq_kdboemq_c H^gZ ba i_j\uo ]bihl_a ijhbkoh`^_gby dhkfbq_kdbo emq_c [ueZ jZajZ[hlZgZ

Wd e = WCVR ~ 1056wj]a68w<


DZd m`_ mihfbgZehkv \h \j_fy iml_r_kl\by dhkfbq_kdbo emq_c hl bo bklhqgbdZ d A_fe_ hgb ijhoh^yl imlv / a ]kf2. Hlkx^Zfh`ghhp_gblv\j_fyL`bagbdhkfbq_kdboemq_c T = L/c ~ 5/10
-26

31010ka1016ka108e_l

]^_ ~ 10-26 ]kf3 iehlghklv f_`a\_a^gh]h \_s_kl\Z k kdhjhklv ^\b`_gbyqZklbpijbgbfZ_lkyjZ\ghckdhjhklbk\_lZL_i_jvfh`gh hp_gblv fhsghklv dhlhjhc h[eZ^Zxl bklhqgbdb dhkfbq_kdbo emq_c P = Wd e. / T ~ 1056 wS]16c = 1040 wS]F


14


DZdb_`_baf_`a\_a^guoh[t_dlh\fh]mlh[_ki_qblvlZdmx fhsghklv" Fhsghklv KhegpZ khklZ\ey_l a 23 wj]k A\_a^ lbiZ KhegpZ \ =ZeZdlbd_ a11 ke_^h\Zl_evgh hgb fh]ml h[_ki_qblv kmffZjgmxfhsghklvebrv34wj]kqlhfgh]hf_gvr_lj_[m_fhc Dhg_qgh \ =ZeZdlbd_ _klv b [he__ fhsgu_ q_f Khegp_ a\_a^u gh bbokmffZjgZyfhsghklv^Ze_dZhllj_[m_fhc

Pk g. = Wd e La40wj]k


Ke_^h\Zl_evgh \kiurdb k\_jogh\uo a\_a^ fh]ml h[_ki_qblv ihklhyggmxbgl_gkb\ghklvdhkfbq_kdboemq_c Fh`_l \hagbdgmlv \hijhk ihq_fm g_ jZkkfhlj_lv \ dZq_kl\_ hkgh\guo bklhqgbdh\ dhkfbq_kdbo emq_c d\ZaZju b jZ^bh]ZeZdlbdb \dhlhjuokh^_j`blky\lukyqbjZa[hevr_dhkfbq_kdboemq_cq_f\ h[uqguo ]ZeZdlbdZo" H^gZdh ohly wg_j]by \u^_ey_fZy d\ZaZjZfb ihjy^dZ wg_j]bb \u^_ey_fhc \k_fb Zdlb\gufb ]ZeZdlbdZfb gh qbkeh d\ZaZjh\ \ 5 jZa f_gvr_ ihegh]h qbkeZ ]ZeZdlbd Dhebq_kl\h `_ jZ^bh]ZeZdlbd ihjy^dZ g_kdhevdbo khl_g l_ \ lukyqm jZa f_gvr_ qbkeZ ghjfZevguo ]ZeZdlbd ihwlhfm bo kmffZjgh_ wg_j]h\u^_e_gb_ hdZau\Z_lky ihjy^dZ gZ ljb f_gvr_ wg_j]h\u^_e_gby\k_o]ZeZdlbd Ijhoh`^_gb_dhkfbq_kdboemq_cq_j_aZlfhkn_jmA_feb GZrZ aZ^ZqZ ^Zlv \ hkgh\ghf dZq_kl\_ggmx dZjlbgm ijhoh`^_gby i_j\bqguo dhkfbq_kdbo emq_c q_j_a a_fgmx Zlfhkn_jmL_f`_dh]haZbgl_j_km_lih^jh[gZydZjlbgZijhp_kkh\ \hagbdZxsbo\Zlfhkn_j_ijbijhoh`^_gbbq_j_ag__i_j\bqgh]h baemq_gby ij_^eZ]Z_f ihagZdhfblvky k mq_[gufb ihkh[byfb [1,2,3,4]. BlZd gZ \_jogxx ]jZgbpm Zlfhkn_ju A_feb ihke_ ^ebl_evgh]h iml_r_kl\by ijboh^yl qZklbpu i_j\bqgh]h dhkfbq_kdh]h baemq_gby Bf ij_^klhbl ij_h^he_lv ^h mjh\gy fhjy ih\_jlbdZeb ihqlb]kf2 \_s_kl\Z\lh\j_fydZd\dhkfhk_ \_kv bo imlv khklZ\be ]kf2 :lfhkn_jZ A_feb khklhbl \ hkgh\ghf ba ZahlZ 12 a fZkk b dbkehjh^Z 22 a fZkk b
15


m]e_dbkeh]h]ZaZIehlghklvZlfhkn_jugZmjh\g_fhjy]kf3. GZ\ukhlZoihjy^dZg_kdhevdbo^_kyldh\dbehf_ljh\a6 kf hl ih\_joghklb A_feb i_j\bqgu_ dhkfbq_kdb_ emqb \aZbfh^_ckl\mxl k y^jZfb Zlhfh\ \ha^moZ < wlbo \aZbfh^_ckl\byo jh`^ZxlkyjZaebqgh]hjh^ZqZklbpuibhgudZhguDgmdehg Zglbgmdehggu_ iZju ]bi_jhgu b l^ DZd ijZ\beh h^gZ ba \lhjbqguo qZklbp lh]h `_ lbiZ qlh b i_j\bqgZy ihemqZ_l \ kj_^g_f hdheh gZqZevghc wg_j]bb lZd gZau\Z_fuc wnn_dl eb^bjh\Zgby Ihwlhfm lZdZy qZklbpZ \ khklhygbb _s_ g_kdhevdh jZa ijh\aZbfh^_ckl\h\Zlv \ Zlfhkn_j_ I_j\bqguc gmdehg k wg_j]b_c !12 w< fh`_l bkiulZlv ^h ^_kyldZ lZdbo ihke_^h\Zl_evguo klhedgh\_gbc k y^jZfb Zlhfh\ \ha^moZ =_g_jbjh\Zggu_ \ wlbo \aZbfh^_ckl\byo aZjy`_ggu_ ibhgu ± aZl_f beb jZkiZ^Zxlky beb fh]ml kZfb ijh\aZbfh^_ckl\h\Zlv k y^jZfb _ckl\bl_evgh wg_j]by dhlhjmx ihemqZ_l wlZ iZjZ d\Zglh\ fgh]h [hevr_ fZkku ihdhy g_cljZevgh]h ibhgZ 0 aFw< b ke_^h\Zl_evgh^eylZdbo -d\Zglh\gZb[he__\_jhylgufijhp_kkhf \aZbfh^_ckl\by kh kj_^hc [m^_l h[jZah\Zgb_ we_dljhg ihabljhgguoiZj_+_-) . We_dljhgu \ k\hx hq_j_^v aZ kq_l lhjfhagh]h baemq_gby gZ y^jZo Zlhfh\ \ha^moZ ^Zxl hiylv \ukhdhwg_j]bqgu_ d\Zglu l_ +- hiylv _ _ iZjm b l^ LZdbf h[jZahf \ \ha^mo_ ihy\ey_lky we_dljhgghnhlhggucdZkdZ^ BlZd fu \b^bf qlh \ Zlfhkn_j_ jZa\b\Z_lky \hi_j\uo dZkdZ^ ba y^_jghZdlb\guo qZklbp ibhgu dZhgu gmdehgu b l^ b, \h\lhjuo we_dljhgghnhlhgguc dZkdZ^ aZ kq_l ijhp_kkh\ lhjfhagh]hbaemq_gbybh[jZah\ZgbyiZjjbk

16


JbkJZa\blb_dZkdZ^gh]heb\gyhli_j\bqghcdhkfbq_kdhcqZklbpu\ Zlfhkn_j_ :±\_jogyy]jZgbpZZlfhkn_ju±i_j\bqgZyqZklbpZ ijhlhg ±\lhjbqgZy eb^bjmxsZy qZklbpZ gmdehg ± y^_jgu_ \aZbfh^_ckl\by ibhgh\ ± y^_jgu_ \aZbfh^_ckl\by [_a h[jZah\Zgby j_eylb\bklkdbo qZklbp ± jZkiZ^ g_cljZevgh]h ibhgZ \hagbdgh\_gb_ we_dljhfZ]gblgh]h dZkdZ^Z ± jZkiZ^ aZjy`_gguoibhgh\\hagbdgh\_gb_fxhggh]hdhfihg_glZ ±\aZbfh^_ckl\b_ \ukhdhwg_j]bqguoqZklbpky^jZfbZlhfh\\ha^moZ

BlZd fu \b^bf qlh \ Zlfhkn_j_ jZa\b\Z_lky \hi_j\uo dZkdZ^ ba y^_jghZdlb\guo qZklbp ibhgu dZhgu gmdehgu b l^ b, \h\lhjuo we_dljhgghnhlhgguc dZkdZ^ aZ kq_l ijhp_kkh\ lhjfhagh]hbaemq_gbybh[jZah\ZgbyiZjjbk H^gZdh jZafgh`_gb_ qZklbp \ wlbo dZkdZ^Zo h]jZgbqb\Z_lky ijhp_kkZfb ^bkkbiZpbb wg_j]bb >ey y^_jguo dZkdZ^h\ gZ ibhgZo b dZhgZolZdbfb^bkkbiZpbhggufbijhp_kkZfb[m^mljZkiZ^uqZklbp \j_amevlZl_ dhlhjuo \f_klh y^_jghZdlb\guo qZklbp jh`^Zxlky y^_jghiZkkb\gu_ fxhgu b g_cljbgh beb dZd \ kemqZ_ jZkiZ^Z g_cljZevgh]h ibhgZ wg_j]by i_j_c^_l \ we_dljhgghnhlhggmx dhfihg_glmGZijbf_j^eyaZjy`_gguoibhgh\fh`ghihdZaZlvqlh jZkiZ^gucijhp_kk^eygboklZg_lij_h[eZ^Zxsbfdh]^Z bo wg_j]by ^hklb]g_l g_dhlhjhc djblbq_kdhc \_ebqbgu ?dj~ mc2hk0, ]^_ K ]_hf_ljbq_kdZy ^ebgZ hlghkbl_evgh y^_jgh]h \aZbfh^_ckl\by AgZq_gb_ ?dj fh`gh gZclb ba mkeh\by jZ\_gkl\Z ]_hf_ljbq_kdhc^ebguKijh[_]mhlghkbl_evghjZkiZ^Z/jZki:
17


LjZki= c0/ 1- 2 =h, ghwg_j]byibhgh\?djjZ\gZ Edj = mc / 1- 2, blh]^Z
2 2

(6 )

(7 )

Edj =mc h / c0, (7 a ) ]^_ 0 \j_fy `bagb ihdhys_]hky ibhgZ +-, mk2 wg_j]by ihdhy ibhgZ>eygb`gbokeh_\Zlfhkn_juhadfb?dj ~ 1010w< < kemqZ_ we_dljhgghnhlhgguo dZkdZ^h\ ^bkkbiZpby wg_j]bb b^_l aZ kq_l bhgbaZpbhgguo ihl_jv we_dljhgh\ b dhfilhg b nhlhwnn_dlh\ ^ey nhlhgh\ JZa\blb_ we_dljhgghnhlhgguo dZkdZ^h\ ijh^he`Z_lky ^h l_o ihj ihdZ bhgbaZpbhggu_ ihl_jb we_dljhgZgZh^ghcjZ^bZpbhgghc^ebg_ g_ klZgml jZ\gufb wg_j]bb ?dj kZfhc qZklbpu < \ha^mo_ agZq_gb_ djblbq_kdhc wg_j]bb jZ\gh Fw<
= 0 / 1-2 = 0?/ mµk2 .
jZki

(8 )

= c = 0cE / mµc

2

dfD

L_i_jv \b^bf qlh ^h mjh\gy fhjy k \ukhlu ij_bfms_kl\_gghc ]_g_jZpbbfxhgh\adf fh]ml^he_l_lvebrvqZklbpukwg_j]b_c ?! 109 w<
18


GZ bhgbaZpbx \ Zlfhkn_j_ fxhgu l_jyxl \ kj_^g_f hdheh Fw<]-1kf2 < kemqZ_\ we_dljhgm i_j_^Z_lky klhev [hevrZy wg_j]by qlh hg kZf ij_\jZsZ_lky \ [ukljmx qZklbpm LZdb_ we_dljhgugZa\Zgu we_dljhgZfbwe_dljhguh[eZ^Zywg_j]b_c \3 ­ 104w_ckl\bl_evgh mkdhj_gb_ bkiulu\Z_fh_ ijb jZ^bZpbhgghf lhjfh`_gbb fxhgZfb \ Pµ / me Z baemq_gb_ wg_j]bb \ Pµ / me)2 jZa f_gvr_ l_o `_ \_ebqbg ^ey we_dljhgh\ Ihl_jb wg_j]bb gZ baemq_gb_[m^ml -(dE / dx)jZ^ bae. ~ (me / mµ )2 E0.


Ke_^h\Zl_evgh wg_j]by (0 l_jy_fZy fxhghf gZ h^ghc jZ^bZpbhgghc ^ebg_ \ a 2 jZa f_gvr_ q_f l_jy_l we_dljhggZlhc`_^ebg_ LZdbf h[jZahf ihlhd \ukhdhwg_j]bqguo fxhgh\ keZ[h ih]ehsZ_lky \ Zlfhkn_j_ Y^_jghZdlb\gu_ qZklbpu [ukljh ih]ehsZxlky \ Zlfhkn_j_ Ihwlhfm gZ mjh\g_ fhjy \lhjbqgh_ dhkfbq_kdh_ baemq_gb_ khklhbl \ hkgh\ghf ba fxhgh\ `_kldZy dhfihg_glZ we_dljhgh\ b nhlhgh\ fy]dZy dhfihg_glZ Bgl_gkb\ghklv aZjy`_gguo qZklbp gZ mjh\g_ fhjy bf__l ke_^mxsb_agZq_gby^ey\_jlbdZevgh]hihlhdZ J` = 0,8210-2 kf-2k-1kj-1 Jf = 0,3110-2 Ff-2k-1kj-1 Ke_^m_l hlf_lblv qlh khklZ\ `_kldhc dhfihg_glu gZ jZaguo \ukhlZo \ Zlfhkn_j_ g_h^bgZdh\Z GZ mjh\g_ fhjy `_kldZy dhfihg_glZkhklhbl bafxhgh\ZgZ\_jog_c]jZgbp_Zlfhkn_juba ijhlhgh\bqZklbp Ijbk\_jo\ukhdbowg_j]byoi_j\bqghcqZklbpu?0 >105=w< \ Zlfhkn_j_ A_feb qbkeh __ \lhjbqguo ihlhfdh\ \ y^_jguo b we_dljhgghnhlhgguo dZkdZ^Zo ^hklb]Z_l 6-109 qZklbp Wlh y\e_gb_ ihemqbeh gZa\Zgb_ rbjhdh]h Zlfhkn_jgh]h eb\gy R:E QZklbpurbjhdh]hZlfhkn_jgh]heb\gyj_]bkljbjmxlky k ihfhsvx fgh]hqbke_gguo b jZaghh[jZaguo ^_l_dlhjh\ jZaf_s_gguo gZ iehsZ^b \ g_kdhevdh d\Z^jZlguo dbehf_ljh\ Baf_j_gb_ qbkeZ qZklbp jZaghc ijbjh^u \ rbjhdhf Zlfhkn_jghf eb\g_ bo wg_j]_lbq_kdbo b ijhkljZgkl\_gguo oZjZdl_jbklbd iha\hey_l ihemqblv bgnhjfZpbx h oZjZdl_jbklbdZo i_j\bqguo
19


qZklbpbbo\aZbfh^_ckl\byo BlZdgZebqb_mA_feb^h\hevghlheklh]hkehyZlfhkn_ju iha\hey_l i_j\bqguf dhkfbq_kdbf emqZf bkiulZlv fgh]hdjZlgu_ \aZbfh^_ckl\by b jZa\blvky dZkdZ^guf ijhp_kkZf Z lZd`_ y\ey_lky ijbqbghc ihy\e_gby fxhgh\ b rbjhdbo Zlfhkn_jguo eb\g_c Hkgh\gufb bklhqgbdZfb \lhjbqgh]h baemq_gby\Zlfhkn_j_y\eyxlky ^eyfxhgh\jZkiZ^aZjy`_gguoibhgh\ ^eywe_dljhgghnhlhgghcdhfihg_glu Z jZkiZ^g_cljZevguoibhgh\kihke_^mxsbfh[jZah\Zgb_f we_dljhgghnhlhggh]hdZkdZ^Z [ jZkiZ^fxhgh\b \ h[jZah\Zgb_we_dljhgh\fxhgZfb Bamq_gb_e_ilhgghcdhfihg_gludhkfbq_kdh]h baemq_gbygZmjh\g_fhjy Ba\_klgh qlh dhkfbq_kdb_ emqb gZ mjh\g_ fhjy khklhyl \ hkgh\ghf ba e_ilhgh\ ± fxhgh\ b we_dljhgh\ JZaebqby \ k\hckl\Zo we_dljhgh\ b fxhgh\ ohjhrh \b^guijb bamq_gbb ih]ehs_gby wlbo qZklbp \ iehlguo kj_^Zo gZijbf_j \ k\bgp_ @ < ij_^eZ]Z_fhc eZ[hjZlhjghc jZ[hl_ bamqZxlky khklZ\ b bgl_gkb\ghklv dhkfbq_kdh]h baemq_gby gZ mjh\g_ fhjy Z lZd`_ hij_^_ey_lky\j_fy`bagbfxhgh\ihbom]eh\hfmjZkij_^_e_gbx I_j\hgZqZevguc \ZjbZgl ^Zgghc eZ[hjZlhjghc jZ[hlu [ue ij_^eh`_g b hkms_kl\e_g ih^ jmdh\h^kl\hf ijhn_kkhjZ GE=jb]hjh\Z>@ < gZklhys__ \j_fy ijh\_^_gZ ihegZy fh^_jgbaZpby wdki_jbf_glZevghc mklZgh\db aZf_g_gu we_dljhggZy qZklv F bkihevah\Zgb_f kh\j_f_gguo fbdjhko_f b pbnjh\hc bg^bdZpbb Z lZd`_ \ukhdh\hevlgu_ b gbadh\hevlgu_ [ehdb iblZgby Ij_^mkfhlj_gZ dhfivxl_jgZy h[jZ[hldZ wdki_jbf_glZevguo ^Zgguo 4.1. Bamq_gb_khklZ\Zdhkfbq_kdboemq_c MklZgh\dZ k ihfhsvx dhlhjhc bamqZ_lky khklZ\ b bgl_gkb\ghklv jZaebqguo dhfihg_gl dhkfbq_kdbo emq_c khklhbl ba lj_o jy^h\ ]ZahjZajy^guo kq_lqbdh\ =_c]_jZ kh[kl\_ggh b y\eyxsboky ^_l_dlhjZfb baemq_gby jbk < dZ`^hf jy^m
20


gZoh^blky iylv iZjZee_evgh \dexq_gguo kq_lqbdh\ F_`^m jy^Zfb kq_lqbdh\ fh`gh jZaf_sZlv ieZklbgu k\bgph\h]h nbevljZ MklZgh\dZ j_]bkljbjm_l lhevdh lZdb_ kh[ulby dh]^Z h^gZ b lZ `_ qZklbpZijhoh^blq_j_a\k_ljbjy^Zkq_lqbdh\Wlhhkms_kl\ey_lky bkihevah\Zgb_f ki_pbZevghc we_dljhgghc ko_fu ± ko_fu ljhcguo kh\iZ^_gbc >ey wlh]h dZ`^uc jy^ kq_lqbdh\ ih^dexq_g d k\h_fm \oh^m ko_fu kh\iZ^_gbc Ko_fZ kh\iZ^_gbc kjZ[Zlu\Z_l lh]^Z b lhevdhlh]^Zdh]^Zh^gZblZ`_qZklbpZijhc^_lq_j_a\k_ljbjy^Z kq_lqbdh\
JbkKo_fZmklZgh\dbjy^ukq_lqbdh\=_c]_jZko_fZkh\iZ^_gbc kq_lgh_mkljhckl\hblZcf_jk\bgph\ucnbevlj

JZkiheh`_gb_ kq_lqbdh\ b lj_[h\Zgb_ bo h^gh\j_f_ggh]h kjZ[Zlu\Zgby \h \k_o lj_o jy^Zo ko_fZ kh\iZ^_gbc \u^_ey_l \ ijhkljZgkl\_ hij_^_e_gguc l_e_kguc m]he kf jbk J_]bkljbjmxlky lhevdh l_ aZjy`_ggu_ qZklbpu dhlhju_ ijhreb \gmljbl_e_kgh]hm]eZ. LZdmxmklZgh\dmgZau\Zxl l_e_kdhihf K ihfhsvx l_e_kdhiZ gm`gh ihemqblv djb\mx ih]ehs_gby l_ aZ\bkbfhklv bgl_gkb\ghklb dhkfbq_kdh]h baemq_gby hl lhesbgunbevljZ\^ZgghfkemqZ_k\bgpZjbk

21


JbkDjb\Zyih]ehs_gbyqZklbpdhkfbq_kdboemq_c\k\bgp_

Ih baf_g_gbx ih]ehs_gby \ k\bgp_ fh`gh \b^_lv qlh dhkfbq_kdh_baemq_gb_gZmjh\g_fhjykhklhblba ^\mo dhfihg_gl ± fy]dhc dhlhjZy [ukljh ih]ehsZ_lky k\bgphf b `_kldhc dhlhjZy ijhoh^bl ijZdlbq_kdb [_a ih]ehs_gby kf k\bgpZ DZd m`_ mihfbgZehkv \ur_ fy]dZy dhfihg_glZ khklhbl ba we_dljhgh\ b nhlhgh\ dhlhju_ [ukljh ih]ehsZxlky k\bgphf `_kldZy dhfihg_glZ khklhbl ba fxhgh\ < gZklhys__ \j_fy ba\_klgh qlh we_dljhgu b fxhgu hlghkylky d h^ghfm deZkkm qZklbp ± e_ilhgh\ dhlhju_ g_ mqZkl\mxl \ kbevguo \aZbfh^_ckl\byo b y\eyxlky [_kkljmdlmjgufb lhq_qgufb qZklbpZfb 22


lj_[m_fhc klZlbklbdb hklZgh\blv gZ[hj AZibkZlv aZj_]bkljbjh\Zggh_ qbkeh hlkq_lh\ 1 b \j_fy gZ[hjZ W \ k_dmg^Zo Dghidhc ©k[jhkª mklZgh\blv j_`bf ^ey ke_^mxs_]h gZ[hjZ klZlbklbdb IhklZ\blv ihhq_j_^gh k\bgph\u_ nbevlju lhesbghc b kf b baf_jblv khhl\_lkl\mxs__ qbkeh qZklbp b \j_fy gZ[hjZ>Zggu_aZg_klb\lZ[ebpm LZ[ebpZ Hnhjfe_gb_j_amevlZlh\]hmijZ`g_gby

LHESBG: NBEVLJ: Pb


kf 0 1 2 4 10 20

]kf

2

DHEBQ?KL N

Wk

J = N/t

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23


JZkq_lgZynhjfmeZ^eyk ^Z_lky\ujZ`_gb_f>@
N= O O O D + DUFWJ O + G G G

>kf2kl_j@

]^_ a ± ^bZf_lj kq_lqbdZ beb rbjbgZ jy^Z kq_lqbdh\ _keb \ jy^m g_kdhevdh kq_lqbdh\ l ^ebgZ kq_lqbdZ d jZkklhygb_ f_`^mp_gljZfbdjZcgbokq_lqbdh\l_e_kdhiZ :[khexlgZy bgl_gkb\ghklv k\yaZgZ k baf_j_gguf agZq_gb_f bgl_gkb\ghklbdZd-o = J / k (qbkehqZklbpkf2kkl_j KjZ\gblv ihemq_ggu_ agZq_gby -eZ[k b JµZ[k k bf_xsbfbky \ ebl_jZlmj_ wdki_jbf_glZevgufb ^Zggufb kf lZd`_ i gZklhys_]hhibkZgby IjhZgZebabjh\Zlv nhjfm djb\hc ih]ehs_gby k lhqdb aj_gby oZjZdl_jZ \aZbfh^_ckl\by we_dljhgh\ b fxhgh\ \ k\bgp_ H[jZ[hldZ wdki_jbf_glZevguo ^Zgguo ii fh`_l [ulv \uiheg_gZkihfhsvxki_pbZevguodhfivxl_jguoijh]jZff Bamq_gb_m]eh\h]hjZkij_^_e_gbyfxhgh\gZmjh\g_fhjy Fxhgu k wg_j]b_c 109 w< [eZ]h^Zjy bo fZkk_ keZ[h hldehgyxlky dmehgh\kdbf ihe_f Zlhfguo y^_j \ha^moZ b ijZdlbq_kdbg_baemqZxllhjfhaguonhlhgh\ Hkgh\guf \b^hf ihl_jv wg_j]bb fxhgh\ ijb ijhoh`^_gbb bfb \ha^moZy\eyxlkyihl_jbgZbhgbaZpbxZlhfh\>eyj_eylb\bklkdbo qZklbp l_ qZklbp kdhjhklv dhlhjuo Y F \ ^Zgghf kemqZ_ bf_ggh lZdb_ fxhgu fu b j_]bkljbjm_f ihl_jb wg_j]bb gZ bhgbaZpbx Zlhfh\ \_s_kl\Z g_ aZ\bkyl hl wg_j]bb qZklbpu b hij_^_eyxlky \ hkgh\ghf k\hckl\Zfb kj_^u b ^ey ^Zgghc kj_^u hgb ihklhyggu LZd ^ey \ha^moZ ijb ijhoh`^_gbb j_eylb\bklkdhc qZklbp_c ^ebgu imlb jZ\ghc ]kf2 beb ]_hf_ljbq_kdhc ^ebgu imlb]kf2 / \ha^]kf3 103 kf \ha^ ]kf3 fxhg l_jy_l wg_j]bx jZ\gmx Fw< H[hagZqbf wlb ihl_jb wg_j]bb q_j_a . G_kfhljy gZ kjZ\gbl_evgh g_[hevrb_ ihl_jb wg_j]bb fxhgZfb \ \ha^mo_ g_ \k_ fxhgu h[jZah\Zggu_ \ \_jogbo kehyo Zlfhkn_ju A_feb ^hklb]Zxl _z ih\_joghklb >_ckl\bl_evgh l_ ba fxhgh\ m dhlhjuo wg_j]by f_gvr_ q_f (fbg Fw< ]kf2 ]kf2 = 1,8.109w< [m^ml ih]ehsZlvky ;_a kms_kl\_gghc hrb[db fh`gh kqblZlv qlh hkgh\gZy qZklv fxhgh\ ^hklb]ZxsZy
24


mjh\gy fhjy aZjh`^_gZ \ \_jog_f keh_ Zlfhkn_ju ^h ^Z\e_gby ± ]kf2 GZ jbk mkeh\gh ihdZaZg kehc Zlfhkn_ju lhesbghc [ \ dhlhjhf \ hkgh\ghf h[jZamxlky fxhgu Fxhg ]_g_jbjh\Zgguc \ keh_ [ ijhoh^bl hl lhqdb ]_g_jZpbb ^h mjh\gygZ[ex^_gbyimlv
/(¨ ) = / &RV¨

(9 )

JbkImlvfxhgZ\Zlfhkn_j_

GZ wlhf imlb fxhg bkiulu\Z_l dZd ihl_jb wg_j]bb gZ bhgbaZpbx Zlhfh\ \ha^moZ lZd b bf__l \hafh`ghklv jZkiZklvky H[Z wlb nZdlhjZ ijb\h^yl d mf_gvr_gbx bgl_gkb\ghklb fxhgh\ k jhklhf a_gblgh]hm]eZ Wdki_jbf_glZevgu_ ^Zggu_ b jZkq_lu ihdZau\Zxl qlh h`b^Z_fh_ m]eh\h_ jZkij_^_e_gb_ fxhgh\ -1 \ke_^kl\b_ bo ih]ehs_gby \ Zlfhkn_j_ A_feb lhevdh baaZ bhgbaZpbhgguo ihl_jv[_amq_lZbojZkiZ^Z [m^_l J1 J(0)cos()


(10)

]^_- bgl_gkb\ghklvfxhgh\ijb = Z = 1,65. Ijhp_kk jZkiZ^Z fxhgh\ k wg_j]b_c ( oZjZdl_jbam_lky ijh[_]hfjZkiZ^Z/jZkib\_jhylghklvxjZkiZ^ZgZimlb/ Z/ L
jZki

= c = c0 E / mµ c2 ,
-L /LjZki

(11) (12)

w(L) = 1 ­ e

,

< dZq_kl\_ \_ebqbgu ( \havf_f lm fbgbfZevgmx wg_j]bx dhlhjZy g_h[oh^bfZ fxhgm ^ey ^hklb`_gby mjh\gy gZ[ex^_gby hl lhqdb]_g_jZpbbg_jZkiZ\rbkv(fbg = / / FRVblh]^Z
25


LjZki = c 0L(0) / mµc cos
2

(13)

Ijb mq_l_ jZkiZ^Z fxhgZ gZ imlb / aZ\bkbfhklv -) [m^_l hij_^_eylvky [he__ \ukhdhc kl_i_gvx ijb FRV, l_ \ ^_ckl\bl_evghklbfh`ghh`b^Zlv - - cos ,
n

(14)

]^_n >1,6. GZc^_f l_i_jv \j_fy `bagb fxhgZ Wdki_jbf_glZevgh fu hij_^_ey_f bgl_gkb\ghklb fxhgh\ - ijbr_^rbo gZ mjh\_gv gZ[ex^_gby ih \_jlbdZeb b ih^ jZagufb m]eZfb , - Imlb dhlhju_ijhrebfxhgu\Zlfhkn_j_, jZaebqZxlkygZ\_ebqbgmØ/ Ø/ L()-L(0)= L(0)(1/cos - 1) kf15) /

LpZki

). (17)

IjbjZ\gy\h[Z\ujZ`_gby^eyØ- ( (16 b17)), ihemqbf J1 ±H-Ø Hlkx^Z / jZki = k´ /(¨ ) = - (¨ ) P ¬ OQ - (¨ ) /() F FRV¨ (19)
/

LpZki

) = J1 -

(18)

26


- P F P¬ F - FRV¨ ¬ FRV¨ ´ = â = â F( fbg F¥ - (¨ ) - (¨ ) OQ OQ - (¨ ) - (¨ )



(20)

>ey ihemq_gby m]eh\h]h jZkij_^_e_gby b \j_f_gb `bagb fxhgh\ kem`bl dZd b \ i_j\hf mijZ`g_gbb mklZgh\dZ k ©l_e_kdhihfªHkvl_e_kdhiZfh`ghgZdehgylvgZaZ^Zggucm]heih hlghr_gbxd\_jlbdZeb H^gZdh \ wlhf \ZjbZgl_ mklZgh\db mql_gu g_dhlhju_ ki_pbZevgu_lj_[h\Zgby Zggu_aZg_klb\lZ[ebpm

27


Hnhjfe_gb_j_amevlZlh\]hmijZ`g_gby
M=HE°

LZ[ebpZ

DHEBQ?KL N

Wk

J = N/t

0° 30 50 70 90

° ° ° °

H[jZ[hldZj_amevlZlh\ Ihkljhblv ihemq_ggh_ wdki_jbf_glZevgh_ jZkij_^_e_gb_ Jwdki KjZ\gblv_]hknmgdpb_c-) Cos2. ey wlh]h gZ ihkljh_gguc ]jZnbd -wdki( gZg_klb ]jZnbd -1 - Cos1,6]^_- -wdki( ijb = 00. Hij_^_eblv \j_fy `bagb fxhgZ D ^ey jZaguo agZq_gbc a_gblgh]hm]eZ > 00. Hij_^_eblv Z[khexlgmx bgl_gkb\ghklv ,o \_jlbdZevgh]h ihlhdZ fxhgh\ gZ mjh\g_ fhjy KjZ\gblv kh agZq_gb_f ihemq_gguf\i_j\hfmijZ`g_gbb LZd `_, dZd b \ mijZ`g_gbb h[jZ[hldm wdki_jbf_glZevguo ^Zgguo b ihemq_gb_ j_amevlZlh\ kh]eZkgh ii fh`gh ijh\_klb k ihfhsvxdhfivxl_jguoijh]jZff
28


EBL?J:LMJ: 1. JZdh[hevkdZy B< DZefudh\ GG K\_jlbeh\ KB <\_^_gb_ \ nbabdm dhkfbq_kdbc emq_c dhgki_dl e_dpbc qZklv , F MGP >HFhkd\Z 2. JZdh[hevkdZy B< DZefudh\ GG <\_^_gb_ \ nbabdm dhkfbq_kdbc emq_c dhgki_dl e_dpbc qZklv ,,, F MGP >H 2004. DZefudh\GGDhkfbq_kdb_emqb k\_jo\ukhdbo wg_j]bc Pbde e_dpbc ih ijh[e_fZf nbabdb dhkfbq_kdbo emq_c \ukhdbo b k\_jo\ukhdbowg_j]bcFBa^\hFhkdmglZ 4. Fmjabg
29