MHB Total Angular Momentum of a Tractrix

[Dr Edward]

I have a 5.0 m tractrix and am trying to work out angular momentum and total angular momentum for two hitchpoint speeds 60 & 70 km/h.
My result shows a higher total angular momentum for the lower speed.
This is not what I expected.
Here are my equations
Positions:
View attachment 8589
Derivatives
View attachment 8590
Angular velocity
View attachment 8591
Angular Momentum
View attachment 8592
TOTAL ANGULAR MOMENTUM
View attachment 8593
If anyone can help spot the error I would be extremely grateful

 

[Dr Edward]

I have spotted the error but don't know how to fix it.
The equation for L(t) is for instantaneous angular momentum.
Momentum is cumulative. i.e. if I add an impulse (F*t) to the classic linear analogy I impart momentum. Newton's 1st law says it will go on forever.
If I now hit it with the same impulse I will double the momentum.
Is there any mathematical genius that will convert the equation for instant angular momentum (L(t)) to total or cumulative momenta.

I should be ever so grateful.