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Side Slip (AKA lateral velocity)
and numerical integration
Lateral acceleration required to follow a curve = V*V/R,
where V is speed and R is curve's radius,
and then there is lateral acceleration actually currently being developed.
Some call that difference "side slip rate", as calculated by
AccelerationSway - SpeedKmh * OrientationYawVelocity,
which integrated over time yields "lateral velocity".
That numerical integration of
side slip rate is problematic
in that errors can accumulate.
Most traditional numerical integration techniques fail for near real time,
wanting information about future samples.
Lacking those, perform simple-minded accumulation.
To minimize error accumulation,
note that side slip should approach zero
for small steering angles and lateral accelerations.
Consequently, apply lowpass filtering to accumulation,
introducing zero values with time constant decreasing
as steering angles and lateral accelerations approach zero.
Simplifying Approximation
"Most drivers are acutely sensitive to the rate of change of body slip angle."
[the Side Slip Angle Rate]
- Damian Harty, Vehicle Dynamics Engineer and Author
in which case, do not bother with numerical integration...
Side Slip Angle Rate factors speed out of side slip rate:
AccelerationSway/SpeedKmh - OrientationYawVelocity.
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