Let's say I have the parametric equations
x(θ)=dcos(θ)+cos(pθ)
and
y(θ)=dsin(θ)+sin(pθ)
to model the path of the moon. Would it be possible to measure the distance that it travels using the aforementioned formulas or in combination with others?
Thanks.
Posted Jan 10, 2016, 6:09 PM UTC
Yes, if you are a calculus 2 student it would be beneficial that you ignore all the other links and comments in the thread so far and think about how you would do it yourself. It's a pretty standard, and valuable, exercise to derive the arc length formula of at least a function of the form y = f(x) yourself and arc length of a parametric equation is not that much harder after.
Thanks, but I'm just a High School student.
...
To give a one-sentence summary of what people have linked to:
Yes. Reparametrize the curve as necessary so that it's derivative has length 1 everywhere. Then the distance along the path between points p(t2) and p(t1) is t2 - t1.
Thanks.
http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength.aspx
Thank you! This really helped.