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2 dni temu · When there is no resistance proportional to the velocity (γ = 0), the Duffing equation can be integrated upon multiplication by the velocity: x˙(x¨ +ω20x + βx3) = d dt(1 2 x˙2 + 1 2 ω20x2 + 1 4 βx4) = 0. x ˙ ( x ¨ + ω 0 2 x + β x 3) = d d t ( 1 2 x ˙ 2 + 1 2 ω 0 2 x 2 + 1 4 β x 4) = 0. Integration yields.
4 dni temu · ParametricPlot[{3.7*Cos[theta] + Cos[3.7*theta], 3.7*Sin[theta] - Sin[3.7*theta]}, {theta, -4*Pi, 4*Pi}, PlotLabel -> "Hypocycloid with k = 4.7"] If k is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius R − 2r .
3 dni temu · sigma=s, absolute_sigma=True. Parameters order of magnitude are alike, fitness is good: But this fit is very sensitive to noise and initial guess which is expected as it must solve a stiff ODE for each point of the curve. It also seems that multiple combination of parameters can lead to equivalent fitness.
4 dni temu · Y = α +β1X1 +β2X2 + u Y = α + β 1 X 1 + β 2 X 2 + u. and I want to determine how much the variables contribute to Y Y on average. Put in other words, I want to decompose the explained variance in Y Y in the contributions of the two explanatory variables.
2 dni temu · Also, they satisfy the orthogonality condition for fixed n with weight w = 1/(1 - x²): \[ \int_{-1}^1 \frac{P_n^i (x) \, P_n^m (x)}{1 - x^2} \,{\text d} x = \begin{cases} 0 , & \ \mbox{for} \quad m\ne i, \\ \frac{(n+m)!}{2(n-m)!}, & \ \mbox{for} \quad m = i \ne 0 , \\ \infty , & \ \mbox{for} \quad m = i =0.
1 dzień temu · The equation of trajectory of a projectile is \(y = 16x - \frac{{5{x^2}}}{4}\). Find the horizontal range.
2 dni temu · Chaos theory. An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
