Double Pendulum Motion: Plotting theta2 vs Time

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SUMMARY

The discussion focuses on the implementation of the Runge-Kutta fourth order method in Python to simulate the motion of a double pendulum. The user, thespaceman, is experiencing issues with the plot of theta2 (the angle of the second rod) versus time, questioning its accuracy. A key insight provided is the importance of checking the conservation of total energy in the system to identify potential numerical problems in the simulation.

PREREQUISITES
  • Python programming proficiency
  • Understanding of the Runge-Kutta fourth order method
  • Basic principles of classical mechanics, specifically pendulum motion
  • Familiarity with data visualization libraries in Python, such as Matplotlib
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  • Investigate energy conservation in numerical simulations of dynamical systems
  • Explore advanced numerical methods for solving differential equations
  • Learn about the effects of numerical instability in simulations
  • Study data visualization techniques for better representation of dynamic systems
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Physicists, computational scientists, and developers interested in simulating physical systems and improving numerical methods for dynamic simulations.

thespaceman
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Hello all,
I have written a python code implementing the Runge-Kutta fourth order method for higher orders to approximate the motion of a double pendulum. The problem I am having is that my plot of theta2 (angle of second rod) Vs time looks a little off and I am curious if I have it correct.
Attached is a graph of both rod angles Vs time. The blue is the first rod and the green is the second rod. I figure the opinion of some physicists may be insightful. Thanks :)
-thespaceman
 

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  • DoublePendulum_N-1000000_1stIC.png
    DoublePendulum_N-1000000_1stIC.png
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Physics news on Phys.org
It's not so easy to see just from the plot, whether there are numerical problems or not. A good check is, whether the total energy of the system remains conserved in the numerical simulation.
 

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