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...
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:
Derivatives
Angular velocity...
Hello Klaas,
Hate to be a nuisance but I had a thought.
Is it possible that the sloped hitch line has a y-intercept?
That might explain why the tractrix cusp does not stay on the y-axis.
Would love an answer. A solution? Even better.
Thanks for your input so far.
Edward
Nice curves - thank you very much.
I have to add a value (shown at the red dot in the picture) to align the cusp to P(0,5).
Also when I change the slope the cusp needs adjustment.
Any idea why this should be?
Once again, thanks for bringing me this far.
Edward
Sorry to trouble you again.
I graphed your equations and got the same result as you. (exciting for me).
Then I played with the coefficients and could not get the position I am looking for.
Here's the MathCad result with different numbers.
What am i doing wrong?
Here's where I want to be:
Hope...
Thank you very much. That is indeed helpful.
Here is an excerpt from Sreenavisan
In all his brilliance he makes the integrating task like getting an ice cream.
I tried MathCad and the result was kilometres long.
My knowledge of maths is not that good to simplify.
I need an equation y=f(x) or...
The cusp of the tractrix is on the y-axis.
I have been studying Sreenavisan et al (Mechanism and Machine Theory 45 (2010) 454–466)
Email me for copy, if needed.
What I need is the equation of a tractrix with the hitch point not on the x-axis but on a line below (y=-mx).
Any help would be...