Double Pendulum Motion: Plotting theta2 vs Time

In summary, the speaker is seeking insight on their implementation of the Runge-Kutta fourth order method to approximate the motion of a double pendulum. They have attached a graph of the angles of both rods over time and are wondering if there are any numerical problems, and if the total energy of the system remains conserved in the simulation.
  • #1
thespaceman
11
0
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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  • #2
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.
 

Related to Double Pendulum Motion: Plotting theta2 vs Time

1. What is a double pendulum?

A double pendulum is a physical system consisting of two pendulums attached to each other. It is a simple mechanical system that exhibits chaotic and unpredictable behavior due to its sensitive dependence on initial conditions.

2. How does a double pendulum move?

The motion of a double pendulum is determined by the forces acting on the system, specifically gravity and tension in the pendulum strings. As the pendulums swing, they create a complex pattern of motion that is difficult to predict.

3. Why is plotting theta2 vs Time useful in understanding double pendulum motion?

Plotting theta2 (angle of the second pendulum) against time allows us to visualize and analyze the changing motion of the double pendulum over time. It can also help us to identify patterns and understand the chaotic nature of the system.

4. How do initial conditions affect the motion of a double pendulum?

The initial conditions, such as the starting positions and velocities of the pendulums, have a significant impact on the motion of a double pendulum. Even small changes in these conditions can result in vastly different trajectories and behaviors of the system.

5. Can the motion of a double pendulum be predicted?

Due to its chaotic nature, the motion of a double pendulum cannot be predicted with complete accuracy. However, mathematical models and simulations can provide some insight into the behavior of the system and help us understand its complex motion.

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