Expression 30: "m" Subscript, "e" , Baseline equals StartFraction, "v" Subscript, "a" "d" "d" "y" "a" "b" , Baseline Over "v" Subscript, "a" "d" "d" "x" "a" "b" , Baseline , EndFraction Add slider for "v" Subscript, "a" "d" "d" "y" "a" "b" , Baseline and "v" Subscript, "a" "d" "d" "x" "a" "b" , Baselineme=vaddyabvaddxab
add slider:
30
Calculating the influence of each point A,B,C,D on point E.
31
Expression 32: "i" Subscript, "a" , Baseline equals StartFraction, 1 Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "a" , Baseline , "y" Subscript, "a" , Baseline , right parenthesis , right parenthesis squared , EndFractionia=1distance0,0,xa,ya2
equals=
0.0 0 2 7 6 6 3 0 9 3 7 8 5 20.00276630937852
32
Expression 33: "i" Subscript, "b" , Baseline equals StartFraction, 1 Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "b" , Baseline , "y" Subscript, "b" , Baseline , right parenthesis , right parenthesis squared , EndFractionib=1distance0,0,xb,yb2
equals=
0.0 0 2 2 7 0 1 0 8 7 3 5 20.0022701087352
33
Expression 34: "i" Subscript, "c" , Baseline equals StartFraction, 1 Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "c" , Baseline , "y" Subscript, "c" , Baseline , right parenthesis , right parenthesis squared , EndFractionic=1distance0,0,xc,yc2
equals=
0.0 0 6 7 5 9 5 0 9 3 8 3 8 30.00675950938383
34
Expression 35: "i" Subscript, "d" , Baseline equals StartFraction, 1 Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "d" , Baseline , "y" Subscript, "d" , Baseline , right parenthesis , right parenthesis squared , EndFractionid=1distance0,0,xd,yd2
equals=
0.0 0 1 2 8 1 9 5 2 2 2 8 2 50.00128195222825
35
Combining the influence vectors of system "AB" and plotting as "rab" (resultant influence of system "AB" upon E).
36
Expression 37: theta Subscript, "a" , Baseline equals sine to the negative 1st power left parenthesis, StartFraction, "y" Subscript, "a" , Baseline Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "a" , Baseline , "y" Subscript, "a" , Baseline , right parenthesis , right parenthesis , EndFraction , right parenthesisθa=sin−1yadistance0,0,xa,ya
equals=
0.4 7 1 4 2 2 5 4 5 4 1 10.471422545411
37
Expression 38: "v" Subscript, "i" "a" "x" , Baseline equals "i" Subscript, "a" , Baseline cosine left parenthesis, theta Subscript, "a" , Baseline , right parenthesisviax=iacosθa
equals=
0.0 0 2 7 6 6 2 1 5 7 4 2 3 30.00276621574233
38
Expression 39: "v" Subscript, "i" "a" "y" , Baseline equals "i" Subscript, "a" , Baseline sine left parenthesis, theta Subscript, "a" , Baseline , right parenthesisviay=iasinθa
Expression 40: theta Subscript, "b" , Baseline equals sine to the negative 1st power left parenthesis, left parenthesis, StartFraction, "y" Subscript, "b" , Baseline Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "b" , Baseline , "y" Subscript, "b" , Baseline , right parenthesis , right parenthesis , EndFraction , right parenthesis , right parenthesisθb=sin−1ybdistance0,0,xb,yb
equals=
negative 0.4 2 7 0 5 3 6 3 6 9 7 2−0.427053636972
40
Expression 41: "v" Subscript, "i" "b" "x" , Baseline equals "i" Subscript, "b" , Baseline cosine left parenthesis, theta Subscript, "b" , Baseline , right parenthesisvibx=ibcosθb
equals=
0.0 0 2 2 7 0 0 4 5 6 7 8 0 60.00227004567806
41
Expression 42: "v" Subscript, "i" "b" "y" , Baseline equals "i" Subscript, "b" , Baseline sine left parenthesis, theta Subscript, "b" , Baseline , right parenthesisviby=ibsinθb
a: left parenthesis, "v" Subscript, "i" "a" "x" , Baseline , "v" Subscript, "i" "a" "y" , Baseline , right parenthesisviax,viay
Label:
equals=
left parenthesis, 0.0 0 2 7 6 6 2 2 , 2.2 7 6 1 times 10 to the negative 5th power , right parenthesis0.00276622,2.2761×10−5
43
b: left parenthesis, "v" Subscript, "i" "b" "x" , Baseline , "v" Subscript, "i" "b" "y" , Baseline , right parenthesisvibx,viby
Label:
equals=
left parenthesis, 0.0 0 2 2 7 0 0 5 , negative 1.6 9 2 times 10 to the negative 5th power , right parenthesis0.00227005,−1.692×10−5
44
Expression 45: "r" Subscript, "a" "b" "x" , Baseline equals "v" Subscript, "i" "a" "x" , Baseline plus "v" Subscript, "i" "b" "x" , Baselinerabx=viax+vibx
equals=
0.0 0 5 0 3 6 2 6 1 4 2 0 3 90.00503626142039
45
Expression 46: "r" Subscript, "a" "b" "y" , Baseline equals "v" Subscript, "i" "a" "y" , Baseline plus "v" Subscript, "i" "b" "y" , Baselineraby=viay+viby
rab: left parenthesis, "r" Subscript, "a" "b" "x" , Baseline , "r" Subscript, "a" "b" "y" , Baseline , right parenthesisrabx,raby
Label:
equals=
left parenthesis, 0.0 0 5 0 3 6 2 6 , 5.8 4 0 5 times 10 to the negative 6th power , right parenthesis0.00503626,5.8405×10−6
47
The same operation for system "CD". To view resultants zoom on "E" as the values returned via the inverse square are very small.
48
49
Expression 50: theta Subscript, "c" , Baseline equals sine to the negative 1st power left parenthesis, StartFraction, "y" Subscript, "c" , Baseline Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "c" , Baseline , "y" Subscript, "c" , Baseline , right parenthesis , right parenthesis , EndFraction , right parenthesisθc=sin−1ycdistance0,0,xc,yc
equals=
5.9 0 5 7 0 7 4 6 0 1 55.90570746015
50
Expression 51: "v" Subscript, "i" "c" "x" , Baseline equals "i" Subscript, "c" , Baseline cosine left parenthesis, theta Subscript, "c" , Baseline , right parenthesisvicx=iccosθc
equals=
0.0 0 6 7 2 3 6 3 3 7 7 8 5 80.00672363377858
51
Expression 52: "v" Subscript, "i" "c" "y" , Baseline equals "i" Subscript, "c" , Baseline sine left parenthesis, theta Subscript, "c" , Baseline , right parenthesisvicy=icsinθc
equals=
0.0 0 0 6 9 5 4 9 6 8 8 8 3 1 50.000695496888315
52
c: left parenthesis, "v" Subscript, "i" "c" "x" , Baseline , "v" Subscript, "i" "c" "y" , Baseline , right parenthesisvicx,vicy
Expression 54: theta Subscript, "d" , Baseline equals sine to the negative 1st power left parenthesis, StartFraction, "y" Subscript, "d" , Baseline Over distance left parenthesis, left parenthesis, 0 , 0 , right parenthesis , left parenthesis, "x" Subscript, "d" , Baseline , "y" Subscript, "d" , Baseline , right parenthesis , right parenthesis , EndFraction , right parenthesisθd=sin−1yddistance0,0,xd,yd
equals=
negative 2.5 6 8 1 8 5 6 6 0 7 9−2.56818566079
54
Expression 55: "v" Subscript, "i" "d" "x" , Baseline equals "i" Subscript, "d" , Baseline cosine left parenthesis, theta Subscript, "d" , Baseline , right parenthesisvidx=idcosθd
equals=
0.0 0 1 2 8 0 6 6 4 6 4 0 90.0012806646409
55
Expression 56: "v" Subscript, "i" "d" "y" , Baseline equals "i" Subscript, "d" , Baseline sine left parenthesis, theta Subscript, "d" , Baseline , right parenthesisvidy=idsinθd
