jh_k123_momentForce

D:\j_Iam_TEMP\_jh\jh_k123_momentForce_v1.wxmx

~/.maxima/deriv.mac и выполнять в Maxima строку load(deriv)$ deriv(какое-нибудь-выражение);

(%i66)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i6)

G1 : 1 ; G2 : 6 ; L1 : 0 ; L2 : 8 ; G : G1 + G2 ; L : 10 ;

\[\operatorname{ }1\]

\[\operatorname{ }6\]

\[\operatorname{ }0\]

\[\operatorname{ }8\]

\[\operatorname{ }7\]

\[\operatorname{ }10\]

f(x,N):=do (eqq:sconcat("="),label_G1:sconcat(x),strG1:string('G1),GG1:concat(strG1,eqq,label_G1,'N))

(%i23)

L7 : [ G1 , G2 ] ; U7 : [ ' G1 ] ;

\[\operatorname{ }\left[ 1\operatorname{,}6\right] \]

\[\operatorname{ }\left[ \ensuremath{\mathrm{G1}}\right] \]

(%i55)

concat ( L7 [ 1 ] ) ; sconcat ( L7 [ 1 ] ) ; string ( L7 [ 1 ] ) ; string ( U7 [ 1 ] ) ;

\[\operatorname{ }"1"\]

\[\operatorname{ }"G1"\]

(%i32)

label_unit : concat ( L7 [ 1 ] ) ; label_unit ;
test : L7 [ 1 ] ;
concat ( test ) ;
slabel_unit : sconcat ( test ) ; slabel_unit ;

\[\operatorname{ }"1"\]

\[\operatorname{ }1\]

\[\operatorname{ }"1"\]

fstr(L7):=block([eqq,label_G,strG,GG],
eqq:sconcat("="),
label_G:sconcat(L7),
label_Gn:concat(L7),
strG:string('G),
GG:concat(strG,label_Gn,eqq,label_G,'N),
return (GG));

(%i33)

fstr ( L7 ) : = block ( [ eqq , label_G , label_Gn , strG , GG ] ,
   eqq : sconcat ( "=" ) ,
   label_G : sconcat ( L7 ) ,
   label_Gn : concat ( L7 ) ,
    strG : string ( ' G ) ,
   GG : concat ( strG , label_Gn , eqq , label_G , ' N ) ,
return ( GG ) ) ;

\[\operatorname{ }\operatorname{fstr}\left( \ensuremath{\mathrm{L7}}\right) \operatorname{:=}\]

(%i51)

my_string : fstr ( L7 [ 1 ] ) ; my_string : fstr ( L7 [ 2 ] ) ;

\[\operatorname{ }"G1=1N"\]

\[\operatorname{ }"G6=6N"\]

(%i35)

eqq : sconcat ( "=" ) ;

\[\operatorname{ }"="\]

(%i36)

label_G1 : sconcat ( G1 ) ;

\[\operatorname{ }"1"\]

(%i37)

strG1 : string ( ' G1 ) ;

\[\operatorname{ }"G1"\]

(%i39)

GG1 : concat ( strG1 , eqq , label_G1 , ' N ) ; GG1 ;

\[\operatorname{ }"G1=1N"\]

(%i40)

label_L1 : sconcat ( L1 ) ;

\[\operatorname{ }"0"\]

(%i41)

label_G2 : sconcat ( G2 ) ;

\[\operatorname{ }"6"\]

(%i42)

strG2 : string ( ' G2 ) ;

\[\operatorname{ }"G2"\]

(%i44)

GG2 : concat ( strG2 , eqq , label_G2 , ' N ) ; GG2 ;

\[\operatorname{ }"G2=6N"\]

(%i45)

label_L2 : sconcat ( L2 ) ;

\[\operatorname{ }"8"\]

(%i46)

label_G : sconcat ( G ) ;

\[\operatorname{ }"7"\]

(%i48)

size1 : sqrt ( G1 ) , numer ; size2 : sqrt ( G2 ) , numer ;

\[\operatorname{ }1.0\]

\[\operatorname{ }2.449489742783178\]

(%i49)

del1 : 0 . 5 ;

\[\operatorname{ }0.5\]

(%i65)

draw2d ( xrange = [ − 2 , 13 ] ,
yrange = [ − 5 , 6 ] ,
font      = "Arial" ,
          font_size = 30 ,
title = "jh_k123_momentForce_v1.wxmx" ,
grid = true ,
proportional_axes = xy ,
line_width = 4 , color = black ,
fill_color = "#eeeeee" ,
rectangle ( [ − size1 / 2 + L1 , − size1 / 2 + L1 ] , [ size1 / 2 + L1 , size1 / 2 + L1 ] ) ,
   rectangle ( [ − size2 / 2 + L2 , − size2 / 2 ] , [ size2 / 2 + L2 , size2 / 2 ] ) ,
    points_joined = false ,
   color = red ,
point_size = 1 ,
line_width = 1 . 3 ,
line_type = solid ,
point_type = filled_circle ,
points ( [ [ L1 , 0 ] , [ L2 , 0 ] , [ L , 0 ] , [ ( L1 − L2 ) , 4 ] ] ) ,
   label ( [ GG1 , L1 , − size1 / 2 − del1 ] ) ,
/*    label([strG1,L1-del1*2,-size1/2-del1]), */
    label ( [ GG2 , L2 , − size2 / 2 − del1 ] ) ,
    points_joined = true ,
point_size = 0 . 1 ,
line_width = 1 . 3 ,
line_type = solid ,
points ( [ [ L1 , 0 ] , [ L1 , 4 ] , [ L2 , 4 ] , [ L2 , 0 ] , [ L2 , 4 ] , [ L , 4 ] , [ L , 0 ] ] ) ,
    line_type = solid ,
color = black , line_width = 1 ,
head_both = true ,
head_length = 0 . 4 ,
head_angle = 10 ,
vector ( [ L1 , − 4 ] , [ ( L − L1 ) , 0 ] ) ,
   label ( [ "L1= label_L1 m" , ( L − L1 ) / 2 , − 4 + del1 ] ) ,
   vector ( [ L2 , − 3 ] , [ ( L − L2 ) , 0 ] ) ,
   label ( [ "L2=2 m" , ( L − L2 ) / 2 + L2 , − 3 + del1 ] ) ,
   color = red ,
   vector ( [ ( L1 − L2 ) , 3 ] , [ ( L − ( L1 − L2 ) ) , 0 ] ) ,
   label ( [ "L3=?" , ( L − ( L1 − L2 ) ) / 2 + ( L1 − L2 ) , 3 + del1 ] ) ,
   head_both = false ,
    vector ( [ ( L1 − L2 ) , 4 ] , [ 0 , 3 · del1 ] ) ,
   label ( [ "G=G1+G2=7 N" , ( L1 − L2 ) , 4 . 5 ] ) ,
     /* GPL */
font      = "Arial" ,
          font_size = 16 ,
color = "#0e406e" ,
label_orientation = ' vertical ,
label ( [ "www.k123.org.ua " , 12 , 1 . 3 ] ) ,
label ( [ "Kopanytsia Y (c) 2025" , 12 . 5 , 1 . 3 ] )
) $

-->	mG1 : ( L − L1 ) · G1 ; mG2 : ( L − L2 ) · G2 ;

\[\operatorname{ }10\]

\[\operatorname{ }12\]

-->	L3 : ( mG1 + mG2 ) / G , numer ;

\[\operatorname{ }3.142857142857143\]

-->	label_L3 : sconcat ( L3 ) ;

\[\operatorname{ }"3.142857142857143"\]

-->	fL ( L1 , L2 , G1 , G2 ) : = ( L1 · G1 + L2 · G2 ) / ( G1 + G2 ) ;

\[\operatorname{ }\operatorname{fL}\left( \ensuremath{\mathrm{L1}}\operatorname{,}\ensuremath{\mathrm{L2}}\operatorname{,}\ensuremath{\mathrm{G1}}\operatorname{,}\ensuremath{\mathrm{G2}}\right) \operatorname{:=}\frac{\ensuremath{\mathrm{L1}}\, \ensuremath{\mathrm{G1}}\operatorname{+}\ensuremath{\mathrm{L2}}\, \ensuremath{\mathrm{G2}}}{\ensuremath{\mathrm{G1}}\operatorname{+}\ensuremath{\mathrm{G2}}}\]

-->	fL ( ( L − L1 ) , ( L − L2 ) , G1 , G2 ) , numer ;

\[\operatorname{ }3.142857142857143\]

-->	size1 : sqrt ( G1 ) , numer ; size2 : sqrt ( G2 ) , numer ;

\[\operatorname{ }1.0\]

\[\operatorname{ }2.449489742783178\]

-->	del1 : 0 . 5 ;

\[\operatorname{ }0.5\]

-->

draw2d ( xrange = [ − 2 , 13 ] ,
yrange = [ − 5 , 6 ] ,
font      = "Arial" ,
          font_size = 30 ,
title = "jh_k123_momentForce.wxmx" ,
grid = true ,
proportional_axes = xy ,
line_width = 4 , color = black ,
fill_color = "#eeeeee" ,
rectangle ( [ − size1 / 2 + L1 , − size1 / 2 + L1 ] , [ size1 / 2 + L1 , size1 / 2 + L1 ] ) ,
   rectangle ( [ − size2 / 2 + L2 , − size2 / 2 ] , [ size2 / 2 + L2 , size2 / 2 ] ) ,
    points_joined = false ,
   color = red ,
point_size = 1 ,
line_width = 1 . 3 ,
line_type = solid ,
point_type = filled_circle ,
points ( [ [ L1 , 0 ] , [ L2 , 0 ] , [ L , 0 ] , [ L3 , 4 ] ] ) ,
   label ( [ "G1=+1 N" , L1 , − size1 / 2 − del1 ] ) ,
    label ( [ "G2=+6 N" , L2 , − size2 / 2 − del1 ] ) ,
    points_joined = true ,
point_size = 0 . 1 ,
line_width = 1 . 3 ,
line_type = solid ,
points ( [ [ L1 , 0 ] , [ L1 , 4 ] , [ L2 , 4 ] , [ L2 , 0 ] , [ L2 , 4 ] , [ L , 4 ] , [ L , 0 ] ] ) ,
    line_type = solid ,
color = black , line_width = 1 ,
head_both = true ,
head_length = 0 . 4 ,
head_angle = 10 ,
vector ( [ L1 , − 4 ] , [ ( L − L1 ) , 0 ] ) ,
   label ( [ "L1=10 m" , ( L − L1 ) / 2 , − 4 + del1 ] ) ,
   vector ( [ L2 , − 3 ] , [ ( L − L2 ) , 0 ] ) ,
   label ( [ "L2= label_L2 m" , ( L − L2 ) / 2 + L2 , − 3 + del1 ] ) ,
   color = red ,
   vector ( [ L3 , 3 ] , [ ( L − L3 ) , 0 ] ) ,
   label ( [ "L3=?" , ( L − L3 ) / 2 + L3 , 3 + del1 ] ) ,
   head_both = false ,
    vector ( [ L3 , 4 ] , [ 0 , 3 · del1 ] ) ,
   label ( [ "G=G1+G2=7 N" , L3 , 4 . 5 ] ) ,
     /* GPL */
font      = "Arial" ,
          font_size = 16 ,
color = "#0e406e" ,
label_orientation = ' vertical ,
label ( [ "www.k123.org.ua " , 12 , 1 . 3 ] ) ,
label ( [ "Kopanytsia Y (c) 2025" , 12 . 5 , 1 . 3 ] )
) $

Figure 1:

Variants 2

-->	kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

-->	G1 : 1 ; G2 : 6 ; L1 : 0 ; L2 : 8 ; G : G1 + G2 ; L : 13 ;

\[\operatorname{ }1\]

\[\operatorname{ }6\]

\[\operatorname{ }0\]

\[\operatorname{ }8\]

\[\operatorname{ }7\]

\[\operatorname{ }13\]

-->	mG1 : ( L − L1 ) · G1 ; mG2 : ( L − L2 ) · G2 ;

\[\operatorname{ }13\]

\[\operatorname{ }30\]

-->	L3 : ( mG1 + mG2 ) / G , numer ;

\[\operatorname{ }6.142857142857143\]

-->	label_L3 : sconcat ( L3 ) ;

\[\operatorname{ }"6.142857142857143"\]

-->	fL ( L1 , L2 , G1 , G2 ) : = ( L1 · G1 + L2 · G2 ) / ( G1 + G2 ) ;

-->	fL ( ( L − L1 ) , ( L − L2 ) , G1 , G2 ) , numer ;

\[\operatorname{ }6.142857142857143\]

-->	size1 : sqrt ( G1 ) , numer ; size2 : sqrt ( G2 ) , numer ;

\[\operatorname{ }1.0\]

\[\operatorname{ }2.449489742783178\]

-->	del1 : 0 . 5 ;

\[\operatorname{ }0.5\]

-->

draw2d ( xrange = [ − 2 , 14 ] ,
yrange = [ − 5 , 6 ] ,
font      = "Arial" ,
          font_size = 30 ,
title = "jh_k123_momentForce.wxmx" ,
grid = true ,
proportional_axes = xy ,
line_width = 4 , color = black ,
fill_color = "#eeeeee" ,
rectangle ( [ − size1 / 2 + L1 , − size1 / 2 + L1 ] , [ size1 / 2 + L1 , size1 / 2 + L1 ] ) ,
   rectangle ( [ − size2 / 2 + L2 , − size2 / 2 ] , [ size2 / 2 + L2 , size2 / 2 ] ) ,
    points_joined = false ,
   color = red ,
point_size = 1 ,
line_width = 1 . 3 ,
line_type = solid ,
point_type = filled_circle ,
points ( [ [ L1 , 0 ] , [ L2 , 0 ] , [ L , 0 ] , [ L3 , 4 ] ] ) ,
   label ( [ "G1=+1" , L1 , − size1 / 2 − del1 ] ) ,
    label ( [ "G2=+6" , L2 , − size2 / 2 − del1 ] ) ,
    points_joined = true ,
point_size = 0 . 1 ,
line_width = 1 . 3 ,
line_type = solid ,
points ( [ [ L1 , 0 ] , [ L1 , 4 ] , [ L2 , 4 ] , [ L2 , 0 ] , [ L2 , 4 ] , [ L , 4 ] , [ L , 0 ] ] ) ,
    line_type = solid ,
color = black , line_width = 1 ,
head_both = true ,
head_length = 0 . 4 ,
head_angle = 10 ,
vector ( [ L1 , − 4 ] , [ ( L − L1 ) , 0 ] ) ,
   label ( [ "L1" , ( L − L1 ) / 2 , − 4 + del1 / 2 ] ) ,
   vector ( [ L2 , − 3 ] , [ ( L − L2 ) , 0 ] ) ,
   label ( [ "L2" , ( L − L2 ) / 2 + L2 , − 3 + del1 / 2 ] ) ,
   color = red ,
   vector ( [ L3 , 3 ] , [ ( L − L3 ) , 0 ] ) ,
   label ( [ "L3=?" , ( L − L3 ) / 2 + L3 , 3 + del1 ] ) ,
   head_both = false ,
    vector ( [ L3 , 4 ] , [ 0 , 3 · del1 ] ) ,
   label ( [ "G=G1+G2" , L3 , 4 . 5 ] ) ,
     /* GPL */
font      = "Arial" ,
          font_size = 16 ,
color = "#0e406e" ,
label_orientation = ' vertical ,
label ( [ "www.k123.org.ua " , 12 , 1 . 3 ] ) ,
label ( [ "Kopanytsia Y (c) 2025" , 12 . 5 , 1 . 3 ] )
) $

Figure 2:

-->	kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

-->	G1 : 1 ; G2 : 6 ; L1 : 0 ; L2 : 8 ; G : G1 + G2 ; L : − 1 ;

\[\operatorname{ }1\]

\[\operatorname{ }6\]

\[\operatorname{ }0\]

\[\operatorname{ }8\]

\[\operatorname{ }7\]

\[\operatorname{ }\operatorname{-}1\]

-->	mG1 : ( L − L1 ) · G1 ; mG2 : ( L − L2 ) · G2 ;

\[\operatorname{ }\operatorname{-}1\]

\[\operatorname{ }\operatorname{-}54\]

-->	L3 : ( mG1 + mG2 ) / G , numer ;

\[\operatorname{ }\operatorname{-}7.857142857142857\]

-->	fL ( L1 , L2 , G1 , G2 ) : = ( L1 · G1 + L2 · G2 ) / ( G1 + G2 ) ;

-->	fL ( ( L − L1 ) , ( L − L2 ) , G1 , G2 ) , numer ;

\[\operatorname{ }\operatorname{-}7.857142857142857\]

-->	size1 : sqrt ( G1 ) , numer ; size2 : sqrt ( G2 ) , numer ;

\[\operatorname{ }1.0\]

\[\operatorname{ }2.449489742783178\]

-->	del1 : 0 . 5 ;

\[\operatorname{ }0.5\]

-->

Figure 3:

Created with wxMaxima.

The source of this Maxima session can be downloaded here.