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pendulum_flat

pendulum_flat - impact of a pendulum with a flat rigid...

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H * impact of a pendulum with a flat rigid surface * L 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 ; H * geometry of the pendulum * L L = 1; H * length of the pendulum @ m D * L g = 9.81; H * gravitational acceleration @ m s^2 D * L ro = 7800; H * density @ kg m^3 D * L R = 0.01; H * radius of the hemisphere end @ m D * L m = PiR^2L ro; H * mass @ kg D * L H * angular velocity * L alpha = 8 0,0,theta'' @ t D< ; H * position of CM: C * L xC = H L 2 L * Cos @ theta @ t DD ; yC = H L 2 L * Sin @ theta @ t DD ; rC = 8 xC,yC,0 < ; H * position of the tip A * L xA = L * Cos @ theta @ t DD ; yA = L * Sin @ theta @ t DD ; rA = 8 xA,yA,0 < ; H * velocity of the tip A * L vA = D @ rA,t D ; H * gravitational force at C * L G = 8 0,mg,0 < ; H * impact angle * L thetai = Pi 6; H * mass moment of inertia * L IC = m * L^2 12; IO = IC + m * H L 2 L ^2; H * equation of motion for free fall * L eqI = Simplify @ IO * alpha - Cross @ rC,G 3 DD ; H *------------------* L sol0 = NDSolve @8 eqI 0, theta @ 0 D == 0, theta' @ 0 D == 0 < ,theta, 8 t,0,Infinity < , Method fi 8 EventLocator, "Event" fi H theta @ t D - thetai L<D ; t0 = InterpolatingFunctionDomain @ First @ theta . sol0 1, - 1 DD ; theta0 = H Evaluate @ theta @ t D . sol0 D . t fi t0 1 DD ; omega0 = Chop @H Evaluate @ D @ theta @ t D .sol0,t DD .t fi t0 1 DDD ; vA0 = vA . 8 theta @ t D -> theta0,theta' @ t D fi omega0 < ; v0x = vA0 @@ 1 DD ; v0y = vA0 @@ 2 DD ; Print @ " " D Print @ "before impact" D H * Print @ "t0 = ",t0," @ s D " D * L Print @ "theta0 = ",theta0," @ rad D = ", theta0 * 180 Pi," @ deg D " D Print @ "omega0 = ",omega0," @ rad s D " D Print @ "v0 = ",vA0," @ m s D " D ; Print @ " " D H * thetaplot0 = Plot @ Evaluate @ theta @ t D .sol0 D * 180 Pi, 8 t,0,t0 < ,AxesLabel fi 8 "t @ s D ","theta @ deg D " < ,PlotRange fi Automatic D omegaplot0 = Plot @ Evaluate @ D @ theta @ t D .sol0,t DD , 8 t,0,t0 < , AxesLabel fi 8 "t @ s D ","omega @ rad s D " < ,PlotRange fi Automatic D * L

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AxesLabel fi 8 "t @ s D ","omega @ rad s D " < ,PlotRange fi Automatic D * L before impact theta0 = 0.523599 @ rad D = 30. @ deg D omega0 = 3.83601 @ rad s D v0 = 8 - 1.91801,3.32209,0 < @ m s D Print @ "impact with a flat surface" D H * elastic compression * L E1 = 200 * 10^9; H * elastic modulus @ Pa D * L Sy = 1.12 * 10^9; H * yield strength @ Pa D * L nu = 0.33; H * Poisson's ratio * L Ep = HH 1 - nu^2 L E1 + H 1 - nu^2 L E1 L ^ - 1; H * equivalent elastic modulus * L k1 = 2 H 3 H 1 - nu^2 LL E1Sqrt @ R D ; H * elastic constant Hertz * L CJ = 1.295E^ H 0.736nu L ; H *
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pendulum_flat - impact of a pendulum with a flat rigid...

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