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2

This computation can be carried out using s1 = NDSolve[{(((γ[x] - 1)/2)*(1 - vr[θ]^2 - (vr'[θ])^2)*(2*vr[θ] + (vr'[θ]* N[Cot[θ*Degree]]) + (vr''[θ]))) - (vr'[θ]*(vr[θ]*vr'[θ] + vr'[θ] v''[θ])) == 0, vr[θ1] == vri, vr'[θ1] == vti, WhenEvent[vr[θ] < 0, "StopIntegration"]}, vr, {θ, θc, θs}] Note that the ODE is singular where ...


3

If you were to be more careful in your use and scoping of variables, everything would be fine. {m, k, g, r0} = {1, 1, 9.8, 2}; With[{ Q = 0, coord = {r[t], θ[t]}, T = 1/2 m (r'[t]^2 + r[t]^2 θ'[t]^2), V = 1/2 k (r[t] - r0)^2 - m g r[t] Cos[θ[t]]}, Lagrangiana[T_, V_, Q_, coords_List] := Module[{L = T - V}, (D[D[L, D[#, ...


5

Here, finally, is the direct analog of newVisibleSpectrum from this answer, which can be used to replace ColorData["BlackBodySpectrum"]. ChromaticityPlot; (* pre-load internals *) newBlackBodySpectrum[t_?NumericQ] := With[{planck = 1/((Exp[1.43877696*^7/(# t)] - 1) #^5) &}, XYZColor @@ ({{1.0478112, 0.022886602, -0.050126976}, (* Bradford ...


2

Difficulties encountered in solving the dispersion relation in the Question are due not so much to convergence of the integral as to the branch point in complex γ- space, which occurs where the argument of ArcTanh[] is equal to 1. Based on the related article cited in a comment above, the integration contour {γ, 1, Infinity} must pass below all non-analytic ...



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