Measuring Chaos in a Double Pendulum

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Measuring Chaos in a Double Pendulum. Vasha Dutell, Patrick Freeman, Duncan Luiten, and Professor Eric Torrence UO Undergraduate Research Symposium. Motivation & Background. Simple system, chaotic motion Chaos: small Δ initial ➔ large Δ final - PowerPoint PPT Presentation

Transcript of Measuring Chaos in a Double Pendulum

Measuring Chaos in a Double Pendulum

Measuring Chaos in a Double PendulumVasha Dutell, Patrick Freeman, Duncan Luiten, and Professor Eric TorrenceUO Undergraduate Research Symposium UO Undergraduate Research Symposium Motivation & BackgroundSimple system, chaotic motionChaos: small initial large finalExponential separation characterized by Lyapunov Exponent

UO Undergraduate Research Symposium Two Modes of AttackSimulationMATLAB generatedRunge-Kutta MethodNo FrictionPhysical PendulumDouble-bar pendulumReleased from high angleCircular dots for trackingCasio EX-F1 at ~5 feet600 fps analyzed in MATLAB UO Undergraduate Research Symposium Circle Detection & TrackingCircle Detection Circular Hough Accumulation ArrayCircle DifferentiationAngles Extracted

UO Undergraduate Research Symposium Phase Space Plots UO Undergraduate Research Symposium 4 parameters: ,, , Angle 1 vs. its Angular VelocityChaotic Periodic Lyapunov Exponent4 parameters: ,, , |Z(t)||Z(t0)|etAt least 1 positive to show chaotic behavior

Rosenstein MethodNearest NeighborsTemporal Separation

UO Undergraduate Research Symposium Challenges/ProblemsCameraLightingEnergy FunctionTracking & InterpolationCircle SizesCould Switch Direction

Future AnalysisFractal Dimension of attractorAngle 2 vs. its velocityUse Box-counting method

Special Thanks toProfessor Eric TorrenceBryan BoggsIsaac Hastings HaussProfessor Richard TaylorAlexander Elrich (Simulation)UO Machine Shop PersonnelIan Pilgrim (Box Counting Analysis)

UO Undergraduate Research Symposium Questions?Lyapunov Exponent CalculationAttractor Plot