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Side Slip (AKA lateral velocity) and numerical integration

There is a 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 the difference "side slip rate",
which integrated over time yields "lateral velocity".

Calculate side slip or lateral velocity by integrating side slip rate,
which in turn is calculated by
  AccelerationSway - SpeedKmh * OrientationYawVelocity.

Numerical integration 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.

maintained by blekenbleu