4569846498

218 Multibody Systems Approach to Vehicle Dynamics
Rearranging (4.186) yields the first three equations required to solve the
analysis:
Equation 1 3346f 3 216 4y 31 4z 112.881 (4.187)
Equation 2 2070f 2 1840f 3 216 4x 19 4z 5906.732 (4.188)
Equation 3 63 250f 2 54 970f 3 31 4x 19 4y 415.833 (4.189)
We can now proceed to set up the next set of three equations working from
point H to point D and using the triangle law of vector addition:
{A DH } 1 {A D } 1 {A H } 1 (4.190)
Determining an expression for the acceleration {A H } 1 at point H using values
for { 5 } 1 and {V H } 1 found from the earlier velocity analysis gives
{A H } 1 {A HJ } 1 { 5 } 1 {V H } 1 { 5 } 1 {R HJ } 1 (4.191)
⎡A
⎢
⎢
A
⎣⎢
A
⎡A
⎢
⎢
A
⎣⎢
A
(4.193)
We already have an expression for {A D } 1 in equation (4.181) and can determine
an expression for the relative acceleration {A DH } 1 of point D relative to
point H using values for { 4 } 1 and {V DH } 1 found from the earlier velocity
analysis:
{A DH } 1 { 4 } 1 {V DH } 1 { 4 } 1 {R DH } 1 (4.194)
⎡A
⎢
⎢
A
⎣⎢
A
Hx
Hy
Hz
Hx
Hy
Hz
DHx
DHy
DHz
⎤ ⎡ 0 1.106 3.881 10
⎥ ⎢
⎥
⎢ 1. 106 0 14.
121
⎦⎥
⎢
2
⎣
3. 881 10
14.
121 0
3
⎤ ⎡9.602 10 ⎤ ⎡228 8
⎥ ⎢
⎥ ⎢
⎥
⎢45 743.094 ⎥
⎢
85x
⎦⎥
⎢
⎥
⎣
1605.022
⎦ ⎣⎢
2285x
5z
5y
⎤
⎥
⎥
mm/s
⎦⎥
3
⎤ ⎡ 0 1.446 10
0.
945
⎥ ⎢
⎥
⎢1. 446 10 0 8.
774 10
⎦⎥
⎢
3
⎣
0. 945 8.
774 10
0
⎤ ⎡252.524⎤
⎥ ⎢
⎥ 112.968
⎢
⎥
⎦ ⎣⎢
3219.588 ⎦
⎡ 0 5z
5y
⎤ ⎡ 0 ⎤
⎢
⎥
⎢
⎢
5z
0 5x⎥
228
⎥
mm/s
⎢ ⎥
2 (4.192)
⎢
⎥
⎣
5y
5x
0
⎦ ⎣⎢
8
⎦⎥
2
3 3
2
⎤ ⎡ 48.179 ⎤
⎥ ⎢
⎥ 0.708
⎥
⎢ ⎥
⎥
⎦ ⎣⎢
135.733⎦⎥
⎡A
⎢
⎢
A
⎣⎢
A
DHx
DHy
DHz
⎡ 0
⎢
⎢
⎢
⎣
4z
4y
4z
4x
0
4y
4x
⎤ ⎡128.269⎤
⎡ 44 51
⎥ ⎢ ⎥ ⎢
⎥
1.121
⎢ ⎥ ⎢ 144 51
⎦⎥
⎣⎢
45.535 ⎦⎥
⎢
⎣
144 44
0
⎤ ⎡114
⎤
⎥ ⎢
⎥ 44
⎥
mm/s
⎢ ⎥
2
⎥
⎦ ⎣⎢
51⎦⎥
4z
4y
4z
4x
4y
4x
⎤
⎥
⎥ mm/s
⎥
⎦
2
(4.195)
(4.196)