Give a formula, in terms of \(\displaystyle x(t)\) and \(\displaystyle y(t)\) and and their derivatives, for the curvature for a curve in \(\displaystyle \mathbb{R}^2\) given by \(\displaystyle \alpha(t) = (x(t),y(t)).\)
How can I do this problem? Do I just apply the curvature formula and substitute \(\displaystyle \alpha(t)\) with \(\displaystyle (x(t),y(t)).\)
How can I do this problem? Do I just apply the curvature formula and substitute \(\displaystyle \alpha(t)\) with \(\displaystyle (x(t),y(t)).\)