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- MotiPoin[A_, B_, C0_, r0_, theta0_, b_, alpha_] :=
- Module[{q0, trif, K2, T, h, eq},
- q0 = (C0 r0 Tan[theta0])/B;
- trif = (2 \[Pi] B)/(r0 (A Cos[theta0] + C0 Sin[theta0] Tan[theta0]));
- K2 = (B q0)^2 + (C0 r0)^2;
- T = 1/2 (B q0^2 + C0 r0^2);
- h = Sqrt[(2 T)/K2];
- eq1 = Derivative[1][p][t] == ((B - C0) q[t] r[t])/A;
- eq2 = Derivative[1][q][t] == ((C0 - A) p[t] r[t])/B;
- eq3 = Derivative[1][r][t] == ((A - B) p[t] q[t])/C0;
- eq4 = Derivative[1][psi][
- t] == (Cos[phi[t]] q[t] + p[t] Sin[phi[t]])/Sin[theta[t]];
- eq5 = Derivative[1][phi][t] ==
- r[t] - Cot[theta[t]] (Cos[phi[t]] q[t] + p[t] Sin[phi[t]]);
- eq6 = Derivative[1][theta][t] == p[t] Cos[phi[t]] - q[t] Sin[phi[t]];
- w1 = (Cos[phi[t]] Cos[psi[t]] -
- Sin[phi[t]] Sin[psi[t]] Cos[theta[t]]) p[
- t] - (Cos[psi[t]] Sin[phi[t]] +
- Cos[phi[t]] Cos[theta[t]] Sin[psi[t]]) q[t] +
- r[t] Sin[psi[t]] Sin[theta[t]];
- w2 = (Cos[psi[t]] Cos[theta[t]] Sin[phi[t]] +
- Cos[phi[t]] Sin[psi[t]]) p[
- t] + (Cos[phi[t]] Cos[psi[t]] Cos[theta[t]] -
- Sin[phi[t]] Sin[psi[t]]) q[t] - Cos[psi[t]] r[t] Sin[theta[t]];
- w3 = Cos[theta[t]] r[t] + Cos[phi[t]] q[t] Sin[theta[t]] +
- p[t] Sin[phi[t]] Sin[theta[t]];
- sol = NDSolve[{eq1, eq2, eq3, eq4, eq5, eq6, p[0] == 0, q[0] == q0,
- r[0] == r0, psi[0] == 0, phi[0] == 0, theta[0] == theta0}, {p, q,
- r, psi, phi, theta}, {t, 0, b trif}];
- {x, y} = Flatten[{-((w1 h)/w3), -((w2 h)/w3)} /. sol];
- z = x^2 + y^2;
- If[A < C0 < B || B < C0 < A, Goto[2], Goto[1]];
- Label[1];
- m = FindMinimum[z, {t, 0, 0, b trif}];
- M = FindMinimum[-z, {t, 0, 0, b trif}];
- ra1 = Sqrt[m[[1]]];
- ra2 = Sqrt[-M[[1]]];
- Print["L'erpoloide è contenuta in una corona circolare"];
- Print["avente raggio interno ra1 e raggio esterno ra2"];
- Print["ra1=", ra1]; Print["ra2=", ra2];
- c1 = ParametricPlot[{ra1 Sin[u], ra1 Cos[u]}, {u, 0, 2 \[Pi]},
- AspectRatio -> 1, PlotStyle -> RGBColor[0.8669, 0.258, 0.227]];
- c2 = ParametricPlot[{ra2 Sin[u], ra2 Cos[u]}, {u, 0, 2 \[Pi]},
- AspectRatio -> 1, PlotStyle -> RGBColor[0.925, 0.140, 0.129]];
- Print@Plot[Sqrt[z], {t, 0, b trif}, AxesLabel -> {"t", "ra"}];
- erp = ParametricPlot[{x, y}, {t, 0, b trif}, AspectRatio -> 1,
- PlotRange -> All];
- Print@Show[erp, c1, c2];
- Goto[3];
- Label[2];
- Plot[Sqrt[z], {t, 0, b trif}, AxesLabel -> {"t", "ra"}];
- Print@ParametricPlot[{x, y}, {t, 0, b trif}, AspectRatio -> 1,
- PlotRange -> All];
- Label[3];
- xp = p[t]/Sqrt[2 T] /. sol;
- yp = q[t]/Sqrt[2 T] /. sol;
- zp = r[t]/Sqrt[2 T] /. sol;
- X = (Cos[u] Sin[v])/Sqrt[A];
- Y = (Sin[u] Sin[v])/Sqrt[B];
- Z = Cos[v]/Sqrt[C0];
- el = ParametricPlot3D[{X, Y, Z}, {u, 0, 2 \[Pi]}, {v, 0, alpha},
- Boxed -> False];
- pol = ParametricPlot3D[
- Evaluate[Flatten[{xp, yp, zp}] /. sol], {t, 0, b trif}];
- Print@Show[el, pol]
- ]
- MotiPoin[1, 1.5, 0.5, 3, Pi/4, 1.5, Pi/4]
- MotiPoin[1, 1.5, 0.5, 3, 0.01, 1.5, Pi/100]
- MotiPoin[0.5, 1.5, 1, -3, 0.01, 3.5, Pi]
- MotiPoin[1, 1, 1.5, 3, Pi/4, 2.5, Pi/2]
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