«-» ()». :., , «-»..... «-».., mathcad: -, -.. :,. 8. -,. -,,, -,,..,.,
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1 .,. MATHCAD», «,»
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10 ....., , , /:..., / : :
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14 , :, ;,...., /:
15 5..., / : :
16 (S, ) (S, ) - S S..8, S ><8, S, 8><6 : S>S., -Rksin (..8 Ss) (.,..). (MT ) 8, ( ) 8.,,.
17 (V, ) (V, ). - V V..9., V 9><7 V, ><9 7><6 : V<V., 9><7 Rksin (..9. Vv) (. V,..) (J, ) - (J, ). - J J
18 8.., J ><8 J, 8><6 : J<J. -, - Rksin (.. Jj) - (. J,..) (, ) (, )... (, /) (, /)... - (, / ) (, / ) -.., -
19 9 ( ), ( ).., , -..4., -. =.4 : k :=.5; k :=.5; k :=.5.,..,..,... S i, ; V i, ; j i, :
20 (S, ) : k=; k=,5; k=; k=...4, R, (k=)., =8, 5,., k= ().
21 (V, ) k=; k=,5; k=; k=...5, k= - V(max) 9. - V(m) , (J, ) k=; k=,5; k=; k=...6, -, - k= k=,5.
22 : ,,, (, 4, 5), (,5, ), (,,5),, - P (, ),. P,5, P,,8 P,, n n,,7 n,,4 z, 4, z,6,5 z z,,8, - -,, 7 n n,, n,8, 8 R, S (. ), 4,. D.75 P o.4 S.8
23 n 45 p.7 z.6 n.58 n.8 R S - º 7º. -, - (): j 7 j j : -, V h -, V h D S V h V -, V h V c V c.97 5 V -, V a V h V c V a.8 4. V a V c,. P k.4p o P k.45,.
24 4, P P P P P P P P a. P c -, P z -,. P c 7.65 P z p.765, n P / b Pz, n P P / P b b z P b.454 P r Pr Pr, (,5, 5) Po, (, 75,98) P, S o -, : S o 4.6
25 Pa P const n S S S z n SS S Pr const.. S ( 8,..) i i ( 8-6 ) i i 8 ( 6-54 ) i i 6
26 6 4 ( 54-7 ) i 8 4 i i S... : :
27 7 - (P ) : P =..., - (..) : - - (, ). ( ), -,, ;. - (..4)...4. :
28 8 - "C:\dinamica-mathcadres\indicatornaya- diagramma.txt" ( dinamica-mathcadres -, indicatornaya-diagramma )., - Mathcad, - Calculate Worksheet Tools.. Q:=READPRN( C:\dinamica-mathcadres\ indicatornaya-diagramma.txt ), Q,.. -,,. ( indicatornaya-diagramma.txt),. - Q:= READPRN( C:\dinamica-mathcadres\ indicatornayadiagramma.txt ), indicatornaya-diagramma.txt Q READPRN"C:\dinamica-mathcadres\indicatornaya-diagramma.tx ( ) -.
29 9.7.7 Q :..5. ()
30 , : ; ;. ; L ; L - ; L. : D, [];, [];, [];, [ ]; m, []; m, []; m, []. m, m 4..
31 4.,, -, m /F : - -, (D=6- ) (D=8- ) , m /F : 5 4 m m - (. 4.). - : 4 (. 4.).. L.. -, m. m - m,. m = m - m. : (L / L ) = ( m / m ) (L / L ) = (m / m ).,.4.), - : m = (, -,) m, ; m = (,7-,8) m, :, 4 ; ; -
32 m = m + m.. MathCad - -. : m.66 m. m.75 m m.5 m.75 m m ). m j -, - []: m j m m m j.965 (. 4.) : ; ; ;.
33 , m : 4.. d / D,6-,7,64-,75 d / D,65-,8,7-,9 l / d,45-,65,5-,65 l /d,5-,6,45-,6 b / D,-,,4-,7 h / D,-,5,-, : =,5d ; =,5d ; =,5(d +d ) R; = (d + d ) - +( d - h ) :, ;, ; l -, ; l -, ;, ;, ; R-, ; D,.. : d 5 l d 6 l b 5 h 8 L ,.5 d d 5 R,. B 7
34 4, 79, m []: m.454 m ]:, : B ' ' m M m M ().585 (. 4.), :, : m, : m R, []:
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35 5 R - []: K R.55 []: K.76 K Rk , 4.. P j []: j j -. MathCad) P ji P jii P j P j m j 6 F m j 6 F P j P j P j
36 P j. P ji P jii. 4..,, []. P -,, -, - (. MathCad). : : Q READPRN ("C:\dinamica-mathcadres\indicatornaya-diagramma.txt" ).7.7 Q Q P, -.
37 7 : P P j P P F b P P Pb P Pb b -.,,. - () , j.] ] [.]
38 8 - : , - - []: -, - - []: N - [] : P S -, []: :
39 9 augment b P K P T P N P S augment ) P K P T P N P S P K, P T [.] P N, P S [.]
40 ,, --4-., P K P T = ], = ] Mathcad : P T P T P K P K
41 4 P T P K (),, - 8 7,, - 8, -. thcad. : submatrix(, 8, 7,, ) submatrix(, 8, 7,, ), 8 7. MA submatrix P T 8 7 MB submatrix P K 8 7 submatrix(,, 8,, ) submatrix(,, 8,, ),, - 8. MA submatrix P T 8 MB submatrix P K 8 - stack: P T stack MA MA P K stackmb MB, :
42 4 P T P K : submatrix(, 54, 7,, ) submatrix(, 54, 7,, ), MA submatrix P T 54 7 MB submatrix P K 54 7 submatrix(,, 54,, ) submatrix(,, 54,, ) -, 54. MA submatrix P T 54 MB submatrix P K 54 P T stack MA MA P K stackmb MB P T P K
43 4 : submatrix(, 6, 7,, ) submatrix(, 6, 7,, ), 6 7. MA4 submatrix P T 6 7 MB4 submatrix P K 6 7 submatrix(,, 6,, ) submatrix(,, 6,, ), 6. MA4 submatrix P T 6 MB4 submatrix P K 6 P T4 stack MA4 MA4 P K4 stackmb4 MB4 P T P K , : M P T R M P T R M P T R M 4 P T4 R M augment P T M M M M 4
44 44 P T M M M M M ,.,, M i -,. ( i ) i i -, - - (. 5.). : M M M M M M
45 45 M 4 M M M 5 M 4 M 4 M MK augment M M M M M M M M M M M 4 M 4 M 5 (. ) (), ,, ]
46 46 M max 54.9 M max, []: M min M max.4 M max M max M min , i,,,5,5 R i i i i i, [] :
47 47 M.5M kp M M.5M kp M M.5M kp M 4 M 4.5M kp4 M kpm.5m kp M kpm.5m kp M kp4m.5m kp4 b M augment b M.5M kp M M.5M kp b M M kpm M M M kpm 4 5 M M augment b M M.5M kp4 M 4 M 4 b M M M kp4m M 4 M M
48 ,, [] M max M max, [] M min M max M max M max M min -.
49 49 6. i,, (i = 4) - = 7 / i = 7 / 4 = 8.
50 /i - - 6/i (. 6., ). -, 5: 4 M , : M KP M kp M kp M kp M kp4. 6..
51 5 6.., : Mkpcp mean M KP Mkpcp l 7 l l ,. N e 58 M.8 n 45 n, - ; Ne, ; M. 955 N e M it M it 5.84 n M - :
52 5 MKP MKP ): MKP MKP Mkpcp ,,, : M ip Mkpcp M ip () 5%: M M it M ip M ip M ,. - - (. 6., 6.4) M
53 5 - - >, -. ( )., 4, ) max. <,,, 5 7 min,.. -., (.. 6.):
54 : ; - ; - ; 4 - ; 5 - ; 6 ; 7 -, J : = = + J d/dt J -, (. 7.). - J J J J J J J, J - ; J, J, J, J a, J -,,,,,,.
55 : ; - ; ; 4 - (); 5 - ; 6 ; 7- ; 8 (- ) ; 9,, ; - () ; - (); ; 4 - ; 5 ; 6 ; 7 - ; 8 ; 9 - ; ; - ; ; -. cp max d cp co ; dt M M d J d min co M M d (F ).. 6., J, : 7.,,,5,
56 56 : J [ ]: J,, J ( J J J J ) J J ) (,75,9) (,4,) (,5,75) (,5,5) (,5,7) 7., J 75-9% - J -. J.85 J J.58 m M, [] m M 4 J d cp m M
57 57 d = (...)S -,[] S-, d cp.5 S d cp.5, = 785 ; = 75. : M 75 (. 7.). h = b / a ; a =(,5-) a M. b.495 h M b a M h M.469 d -, : d d cp h M d.4669 d,5-,5,. d, : d d cp h M d.67
58 58 J M =J M : V MO, : J.58 n max.5 n n max 475 n -, - ; n (,4,7) n - ; n (,,5) n - ; n -. V MO : [V ] 7 ; [V ] ; [V ]., -, /; : [ ] 4 ; [ ].
59 59,,. d c.95 d d c d -, (,5-,7)d ; - -, =,-7 - =,8-,. - : [ ] ; [ ].
60 6 8. P S - (. 8.): P T, -, P K,., m,. ). 8.., : ;
61 6 8..., -,,, -, (. 8., )., -,.,,, -. () - P T,. ) ). - R ). 8., ). R -,,.,,,.. 8.., :, ;,, - R,, -
62 6., (, 7), ( R 7 ) (. 8., ). (. 8., )., - 8 (. 8., ).. 8.,,, R,,. :, :, -, ; mr -,, ;,, (. ) Rmax R(hmin), []. R, R max, R (hmin) - (),. R = f).. 8.). R - F, R (- :.8., -,.8., - ). R (hmin),, R = R,. - F.max, R - (.8., '- ) R EF (. 8., ').
63 : R max, - ; R,,., a - ;, -
64 (.8., ).. R, R max, R (hmin). R (hmin) (.8., ) -.,., - R R.8.4). j,.. - index. lim, lim -, -, R R. ( ). lim 9. Mathcad -. R mean R - R R.4 R - R, - R. R submatrix R lim, R - R lim. R R min minr R min.4 R min R, , ').
65 65 j 7; j j - R R R (): j lastr R (. 8.4). ): index j j R j R min R, R j R min R,, -
66 66 R j ): R R (- index 4 - (). area. 8., : area index R j area.7484 j ( index ) - j =. (,, j = (44 ), 4). R.hmin. ): ( area R.hmin. R index.hmin (. 8., )., : R mean R R.4 R (hmin) EF, - R R,,,. - j,.. - index index. R R - index).
67 67 R, R :. 8.5 R. -,, - R R, -. alim blim, -. - : alim blim ). R submatrix R alim blim R - R alim blim. 8.5). R min minr R min.47 R min R, E. 8.5;. 8., ). : j 7 j j R R, - : j j alim, : j -, - alim.
68 (). j lastr j - (), R R (): index j R j R min index 4 j F R R index). blim lim, - F (. 8., '). : blim 8 clim 4,. 8.6). R submatrix R blim clim R - R () blim clim (. 8.6).
69 69 R min minr R min.75 R min R F (. 8.6). j j blim. R. 8.6: n lastr j lastr n n j -. (), R R ( R j ): index j R j R min index j R : indexa index alim indexa 54 indexc index blim indexc ( F).
70 7 area: area indexc R j area.7647 j indexa ( indexc ) - R.hmin.. 8., '): R.hmin. area indexc indexa R.hmin R,,,.,. - Mathcad: i last R, i, R ;
71 7, R, ', R,. (. 8.7). II III II I I, III c III, III : III III IV IV III PTi a cos, Ri III = III +. R (. 8,8, )., - (. 8.8, ) - (. 8.8, ), -, - R 8
72 RR 8 RR ). 8.8., : R ;., -, (. 8.9). -,. -,., -, ,, : k ) a k k 6 b k if a k a k otherwise c k a k if a k otherwise
73 7, : k ; a k, b k - (. 8.9, ); c k - (. 8.9, ); q. q,. 4 b k 6 5 a k ) : ) ; ). ) - r, : maxq ( ), : - ( 5); -, q. r (. 8.). :
74 74 i as i i 6 r rs, : as i ( ). r /+ = 4/, : / - - (. r - ); -. i as i , -, -. - (. 8.),, - ( ),.,, (. 8.).
75 , ). -, -, ' ' ' - (. 8.),
76 R,, '. : R P P'. R b R,, -,. R
77 , ) P T P T P T P T4 4 M PT P K P K P K P K M PK p - i (i+)- p 8 -
78 78 5 P T P T P T P T , ,
79 , K.696 K Rk.897 Rk -, (. ) []:,, :,, - : M augment P T R k P T R k M ,, - : R.5 R k R , :...
80 8 P' T.5 P T K' Pk.5 -, -, -. -,, R , P T PK, : P T P' T K Pk K' Pk 9..., :, :,, - : M a augment P T R k M a 4 5 P T R k
81 8, R P T PK, P T PK, :, P T PK, : P T P' T P' TT K' PkT K Pk K' Pk P' TK K' PkK, : M b augment P T K Pk R M b 4 5 P T K Pk R
82 8 9..., :, :,, - : M a augment P T R k P T R k M a , : p - ; p =, P' T.5 P T K' Pk.5 -, -, - ; -, -. P T PK, P T PK -, :
83 8, P T PK, : P T P' T P' TT K' PkT cos p 8 K Pk K' Pk P' TK K' PkK cos p 8, : R P T K Pk M b augment P T K Pk R M b P T K Pk R (. ) (), -.
84
85 , : R cp mean R R cp mean R R cp. R cp.4 R cp mean R l 7 R cp.979 l l R R cp c l. 9.7.,.. R R cp c l. 9.8.,.
86 86 R R cp c l. 9.9.,. R, R, R, R k,,,, P T, - (. ). - P K k : - R k, -, -. - :
87 87 i lastr - - (. 9.) ,. 9., 8, -,.
88 , : k - : a k, b k - ; c k - q - (, ) - k- q q - -, q r -,
89 89 i : r rs : as i ( ). - r /, -. ( ),.. 9..
90 9., -,., : P =; P j =; K R =; =; j =; R =, j j j, j, K. R -,, P j, P j, R ( ), - (- ) ,.... : ;.
91 9 : R, ; n, /; = R / L : - ; n , n 47.9 (.. 4.). m j -,, - []: m R -,, []: P j : P j = ji + jii, ji = - m R cos; jii = - m R cos. j j
92 9.. P ji - ji. -, - (.. ), -. ) ) ) (.., ) - -,. P ji : PjI = PjI() + PjI() + Pj I() + PjI(4) = c m j R 6 c P ji P ji
93 9 P ji P ji P ji, P ji, P ji, P ji4, j I..., ( P - P j I = ),. -. -, (.., ), : M jipji,5 a; M jipji,5 a; M jipji,5 a; M ji4pji4,5 a., -., - (.., ),, - -. a -, M ji P ji. (.5a) P ji. (.5a) P ji. (.5a) P ji.4 (.5a)
94 94 M ji : M ji P ji. (.5a) M ji P ji. (.5a) M ji P ji. (.5a) M ji4 P ji.4 (.5a) M ji M ji M ji M ji M ji4..4. ji, ji, ji, ji4, j I...4, M., : ji,... P jii jii. P jii = P jii() + P jii() + P jii() + P jii(4) = 4m R cos j, -, -
95 95 (..5, ). (..5, ) (..5, ),. ) ) )..5.. c 6 m j R P jii c cos c cos ( 8) c cos ( 8) c cos 8 P jii 4 c cos 8. P jii.. : P jii P jii. P jii. P jii. P jii.4
96 P jii, P jii, P jii, P jii4, P j II...6, P jii,.. M jii P jii..5a P jii. (.5a) P jii. (.5a) P jii.4 (.5a) M jii : -. M jii P jii. (.5a) M jii P jii. (.5a) M jii P jii. (.5a) M jii4 P jii.4 (.5a) M jii M jii M jii M jii M jii4 M jii..7,..
97 jii, jii, jii, jii4, j II... R R. (.., ) -,. R = R ( ) - R () - R ( ) + R (4) = K R m R R m R R m R R m R R K R, -. R = R (),5 - R (),5 - R (),5 + R (4),5 = M R M R m R R.5 a m R R.5 a.5a m R R.5a m R R, - 8, -.
98 98 - -, 4 (..8) jii - : jii 8 4m R cos = : R m jii m j 4 jii j 4 m ( ) cos jii jii m jii.88..,,-, -,.,5 R(),,,5 R() +,5 R(). - m R, 4, 5, 8 (.., ). -. : m R = m R R/( ).,5 R = m R,5m R R = m R,
99 99.4. :..9. d 5 6 l d 6 l b 5 h 8 B 7 (d,, l, d,, l, b, h, B ). 78 -, h d - ) R R, : h d R R.57 d h R B R.87 b, ():
100 b.5b b., : asin 4 m R b R R R 8.48 m R, : m b R m.7 R 8, : R 4 R R R sin : m.45 m,5 m R R m R R (.., ). (.., ) - = =..
101 ... : - ;, - ; -8.
102 . :./..,..,..,.. ;....-.:, : /..,...; ,..-.:., ,. :..:, :../, -....:..,. 496.: , : -, :.. :, :../.;...., /..,..,..,..,..,.,.; , 964, :,
103 N,, i n, n, D, S,, n n - e R ,4 9,86,5,5,6,89,8,5,8 4R ,95,6,6,55,,5,9,8 4R ,4,,,5,5,5,6,,85 4 5R ,5 9,,5,,6,7,8,,86 5 4R ,5 95,5 9,98,48,5,7,9,7,6,84 6 R ,6 79 8,5,89,9,8,47,,6,9,8 7 6R ,4 8,,55,,7,6,9,,88 8 4R ,8,4,5,,8,65,4,8 9 6R ,,67,,49,5,,7,84 5R ,5,5,58,6,,6,,8,,8 5R ,5,,,7,,,5,8 5R ,9 9 9,5,69,5,,9,65,45,9,8 6R ,4,49,45,,68,9,8,6,8 4 4R ,4,9,,4,,76,75 5 6R ,65,5,5,9,45,8, R ,58,,6,4,58,9,46,8 7 4R ,6,,6,7,6,57,79 8 4R ,7,455,9,9,99,9,,86 9 4R ,58,669,,7,6,4,7,8 6V-9º ,64,57,6,65,4,8,7,8
104 V-9º ,68,46,5,54,4,6,96,8 R ,5 -,49,,8,69,8,99,76 R ,8 -,57,,76,9,8,54,75 4 R ,6,,5,75,,67,74 5 R ,9 -,,,6,5,8,78,7 6 R ,6 -,78,,77,68,6,,7 7 R , -,49,,69,,7,4,78 8 R ,5 -,65,,85,9,4,6,77 9 R ,5,,4,8,78,75,79 R , -,669,9,7,49,8,95,77 R ,5 -,46,,86,65,4,58,78 4,5 8 5, , -,58,,586,78,6,67, , , -,98,,47,8,8,9, ,8 -,55,,68,57,54,45, ,5 -,496,,98,99,67,,74 6 6R ,6, -,,,5,,9,86 7 4R ,7 -,6,7,4,9,,8 8 4R ,5 -,5 4,,57,8,,79 9 4R ,5 85 -,4 4,6,64,7,4,8 4 4R ,5 88,,5 -,5,8,8,46,56,85 4 4R ,6 -,6,7,94,55,75,8 4 4R ,5,5 -,4,4,,64,57,8 4 4R ,8 -,4,9,9,8,8,8 44 4R ,4 86,69 9, -,5,7,77,44,65,78
105 R ,4 86,69 8,7 -,,,54,,8,8 46 4R ,5 9,8 9 -,6,8,47,4,9, R ,4 75,4 9,5 -,4,,9,6,,8 48 4R ,8 -,5,6,46,48,4,8 49 5R , -,,9,57,57,5,84 5 5R , 4,4,6,65,6,78 5 5R ,5 -,4 4,9,74,7,47,8 5 5R ,5 -,,7,8,7,58,79 5 4R , -,6,,97,6,69,8 54 6R ,8 9,5 -,,4,,5,79,8 55 6R ,6 79,6,5 -,,6,9,44,8,8 56 6R ,9 84 9, -,,,88,9,7, R ,9 7,4 -, 4,5,75,7,6,8 58 6V-9º ,5 8 -,,9,64,9,5, V-9º ,4 77 9, -,,6,57,8,45,84 6 6V-9º ,4 69 -,,,4,46,7,8 R V V; i - ; n, - ; N e, ; n, - ; -, ; D, ; S, ; ;, ; - ; - ; ; n - ; n - ; ; - -.
106 6
107 7, j [.]. P N, P S [.],, [] P K, P T [.].
108 .,. MATHCAD., /6. 8. P.... 6, ,.,.., 8
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