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I know how to calculate the lateral and longitudinal velocities given the velocity $v$ and heading angle $\theta$ :

$ v_{lat} = v × \ \mathrm{sin} \theta$

$v_{long} = v× \cos \theta$

But does this extend to acceleration $a$ and jerk $j$, i.e.,

$a_{lat} = a × \sin \theta$

$a_{long} = a × \cos \theta$

$j_{lat} = j × \sin \theta$

$j_{long} = j \cos \theta$

?

Thanks for your time

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Sep 6, 2021 at 16:43
  • $\begingroup$ Basically, I am asking - are these equations equivalent: 1. a_lat = asin(theta) & a_lat = derivative(v_lat) 2. a_long = acos(theta) & a_long = derivative(v_long) 3. j_lat = jsin(theta) & j_lat = derivative(a_lat) 4. j_long = jcos(theta) & j_long = derivative(a_long) ? $\endgroup$ Sep 8, 2021 at 14:58

1 Answer 1

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Yes, since the acceleration and jerk are both vector quantities, your equations should be ok.

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  • $\begingroup$ Thanks a lot. I believe that too, but is there any literature I could read on this? $\endgroup$ Sep 8, 2021 at 14:49

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