particle_flat.nb

# particle_flat.nb - In[724]:= H* packages that have some...

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In[724]:= H * packages that have some differential equations to solve and define some utility functions * L Needs @ "DifferentialEquations`NDSolveProblems`" D ; Needs @ "DifferentialEquations`NDSolveUtilities`" D ; Needs @ "DifferentialEquations`InterpolatingFunctionAnatomy`" D ; Needs @ "GUIKit`" D ; ClearAll @ "Global` * " D ; Off @ General:: spell D ; Off @ General:: spell1 D ; R = 0.01; V = 4 Pi R^3 ê 3; m = 0.0327; E1 = 200 * 10^9; Sy = 1.12 * 10^9; nu = 0.33; Ep = HH 1 - nu^2 E1 + H 1 - nu^2 E1 L ^ - 1; k1 = 2 3 H 1 - nu^2 L E1 R ; g = 9.81; h = 0.1; v0 = Sqrt @ 2 g h D ; H = 3 Sy; H * Chang * L K = 0.454 + 0.41 nu; xc = H Pi K H êH 2 Ep LL ^2 R; H * Jackson * L CJ = 1.295 E^ H 0.736 nu L ; xcJ = H Pi CJ Sy êH 2 Ep LL ^2 R; Print @ "Chang: xc = ", xc, " @ m D " D Print @ "Jackson: xc = ", xcJ, " @ m D " D H * m x'' @ t D == m g - k1 x @ t D ^ H 3. ê 2 L * L eq = m x'' @ t D == m g - k1 H x @ t DL ^ H 3. ê 2 L ; Print @ " " D Print @ "Chang" D ; solC = NDSolve @8 eq, x @ 0 D ã 0, x' @ 0 D ã v0 < , x, 8 t, 0, Infinity < , Method Ø 8 EventLocator, "Event" Ø H x @ t D - 1.9 xc L<D ; tIC = InterpolatingFunctionDomain @ First @ x ê . solC DD@@ 1, - 1 DD ; xIC = Chop @ First @ Evaluate @ x @ t D ê . solC D ê . t Ø tIC DD ; vIC = Chop @ First @ Evaluate @ x' @ t D ê . solC D ê . t Ø tIC DD ; Print @ "tI = ", tIC, " @ s D " D ; Print @ "xI = ", xIC, " @ m D " D ; Print @ "vI = ", vIC, " @ m ê s D " D ; Print @ " " D ; Print @ "Jackson" D ; Print @ " " D ; Print @ "critical values " D ;

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Print @ "xc = ", xcJ, " @ m D " D Pc = k1 xcJ^ H 3. ê 2 L ; Print @ "Pc = k1 xc^ H 3. ê 2 L = ", Pc, " @ N D " D ; PcJ = 4. ê 3 H R ê Ep L ^2 H Pi CJ Sy ê 2 L ^3; Print @ "Pc = 4. ê 3 H R ê Ep L ^2 H Pi CJ Sy ê 2 L ^3 = ", PcJ, "
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## particle_flat.nb - In[724]:= H* packages that have some...

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