I have a list of data pair and want to fit it to a parametric equation. The parametric equation is:
$ h(a) = \frac{a^2}{R}-\sqrt{\frac{2\pi a w}{E^*}}$
$ P(a) = \frac{4a^3E^*}{3R}-\sqrt{8\pi a E^* w}$
where $ R = 25\times10^{-6}$ . The fitting parameters are $ E^*$ and $ w$ . The $ h$ and $ P$ data points are as follows.
hvec=1.*^-9*{-543.788, -534.501, -522.833, -505.644, -487.923, -474.96, -460.52, -442.36, -424.588, -408.419, -394.821, -377.307, -360.71, -346.718, -325.011, -300.86, -282.9, -262.037, -246.88, -224.863, -211.286, -193.259, -175.539, -154.332, -132.628, -113.743, -93.71, -72.768, -46.825, -21.77, 7.576, 30.174, 56.659, 84.041, 106.232, 128.223, 153.729, 183.145, 217.012, 246.052, 270.311, 299.043, 326.504, 345.172, 358.411} Pvec=1.*^-6*{-0.144, -0.243, -0.354, -0.464, -0.589, -0.705, -0.818, -0.936, -1.052, -1.178, -1.284, -1.394, -1.501, -1.608, -1.743, -1.872, -1.972, -2.051, -2.112, -2.203, -2.273, -2.328, -2.406, -2.5, -2.58, -2.651, -2.741, -2.835, -2.944, -3.003, -3.041, -3.077, -3.13, -3.156, -3.163, -3.151, -3.105, -3.066, -2.98, -2.879, -2.8, -2.711, -2.586, -2.462, -2.336} ListPlot[Thread[{hvec,Pvec}], Joined -> True, PlotStyle -> Red] Does anyone have ideas?
