4569846498

232 Multibody Systems Approach to Vehicle Dynamics
Multiplying out the matrices in (4.289) yields the next set of three equations:
Equation 10 15F A31y 239F A31z 1F B31y 239F B31z 42 521f S2 0
(4.290)
Equation 11 15F A31x 115F A31z 1F B31x 115F B31z 69f S2 0
(4.291)
Equation 12 239F A31x 115F A31y 239F B31x 115F B31y 294f S2 0
(4.292)
Consider last Body 4 and the equations required for force equilibrium:
∑{F 4 } 1 {0} 1 (4.293)
{F P41 } 1 {F D34 } 1 {F G24 } 1 f S1 {R JH } 1 {0} 1 (4.294)
⎡ 0 ⎤ ⎡FD34x⎤
⎡FG24x⎤
⎡ 0 ⎤ ⎡0⎤
⎢
0
⎥ ⎢ ⎥ ⎢ ⎥
34
24 1 228 0 N
⎢ ⎥ ⎢
F
⎢ ⎥ ⎢ ⎥
D y⎥
⎢
FG
y⎥
fS
⎢ ⎥ ⎢ ⎥
⎣⎢
10 000⎦⎥
⎣⎢
FD34z⎦⎥
⎣⎢
FG24z⎦⎥
⎣⎢
8 ⎦⎥
⎣⎢
0⎦⎥
(4.295)
The summation of forces in (4.295) leads to the next set of three equations:
Equation 13 F D34x F G24x 0 (4.296)
Equation 14 F D34y F G24y 228f S1 0 (4.297)
Equation 15 F D34z F G24z 8f S1 10 000 (4.298)
Taking moments about point G for the forces acting on Body 4 gives
∑{M G4 } 1 {0} 1 (4.299)
{R PG } 1 {F P41 } 1 {R DG } 1 {F D34 } 1 {R HG } 1 f S1 {R JH } 1 {0} 1
(4.300)
⎡ 0 176 58⎤
⎡ 0 ⎤ ⎡ 0 216
31⎤
⎡F
⎢
176 0 7
⎥ ⎢
0
⎥
⎢
216 0 19
⎥ ⎢
⎢
⎥ ⎢ ⎥ ⎢
⎥ ⎢
F
⎣⎢
58 7 0 ⎦⎥
⎣⎢
10 000⎦⎥
⎣⎢
31 19
0 ⎦⎥
⎣⎢
F
D34x
D34y
D34z
⎡ 0 267 75⎤
⎡ 0 ⎤ ⎡0⎤
f
⎢
1 267 0 163
⎥ ⎢
S 228
⎥
⎢
0
⎥
Nmm
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎣⎢
75 163 0 ⎦⎥
⎣⎢
8 ⎦⎥
⎣⎢
0⎦⎥
(4.301)
Multiplying out the matrices in (4.301) yields the next set of three equations:
Equation 16 216F D34y 31F D34z 60 276f S1 580 000 (4.302)
Equation 17 216F D34x 19F D34z 1304f S1 0 70 000 (4.303)
Equation 18 31F D34x 19F D34y 37 164f S1 0 (4.304)
Finally applying the vector dot product to ensure that no thrust for the force
{F F21 } 1 acts along the axis E–F gives
{F F21 } 1 • {R EF } 1 0 (4.305)
⎤
⎥
⎥
⎦⎥