4569846498

50 Multibody Systems Approach to Vehicle Dynamics
Differentiating this with respect to time yields:
d
{ A } { } {{ } }
t V d
s
PQ 1 PQ 1 2
1 { RPQ} 1 | VPQ
|{ lPQ}
1
d dt
{ A } { } { V } { } { R }
PQ 1 2 1 PQ 1 2 1 PQ 1
s
s
1 1
| VPQ
| d { }
t l PQ | A PQ |{ l PQ}
d
Since
d
d { RPQ t
} { VPQ } { 2
} { RPQ
}
1 1 1 1
it therefore follows that
d
d { lPQ
} { 2
t
} { lPQ
}
1 1 1
(2.121)
(2.122)
(2.123)
(2.124)
and
|VPQ|{l s PQ } 1 {VPQ} s 1 (2.125)
and
|APQ|{l s PQ } 1 {APQ} s 1 (2.126)
Combining these we therefore obtain
{APQ} 1 { 2} 1 { VPQ} 1 { 2} 1 { RPQ} 1 { 2}
1
s
s
{ V } { A }
(2.127)
PQ 1 PQ 1
Substituting
{V PQ } 1 { 2 } 1 {R PQ } 1 {VPQ} s 1 (2.128)
gives the following:
1 2 1 2 1 1 s
1 2 1
{ APQ} { } {{ } { RPQ} { VPQ} } { }
{ R } { } { V s } { A
s }
PQ 1 2 1 PQ 1 PQ 1
It therefore follows that
{ APQ} { } {{ } { RPQ} } { } { RPQ}
2{ } { V
s } { A
s }
1 2 1 2 1 1 2 1 1
2 1 PQ 1 PQ 1
(2.129)
(2.130)
In summary we can now identify all four components of acceleration associated
with the combined rotation and sliding motion as the centripetal
acceleration {APQ} p 1 , the transverse acceleration {APQ} t 1, the Coriolis acceleration
{A c PQ} 1 and the sliding acceleration{APQ} s 1, where
{APQ} p 1 { 2 } 1 {{ 2 } 1 {R PQ } 1 } (2.131)
{A t PQ} 1 { 2 } 1 {R PQ } 1 (2.132)
{A c PQ} 1 2{ 2 } 1 {V s PQ} 1 (2.133)
{A s PQ} 1 |A s PQ| {l PQ } 1 (2.134)