Why Does Restricting a Pendulum's Angle Component Simplify Simulation?

[that_guy]

I've been working on a program that simulates the chaotic action of a pendulum with magnets near the 'bob'. I represent the pendulum as a constant length rod at an angle to the vertical. The angle is a vector, with the direction being the axis it is rotated around and the magnitude being the angle it is rotated.

I finally got it working but only after forcing one of the components of the angle to be zero- the vertical one.

Can anyone explain why this is so? I would've thought that since it is free to rotate around any axis that forcing a component to zero wouldn't be necessary. Having three degrees of freedom is redundant though since only two are needed. What is modeled when using all three components of the angle vector?

 

[eljose79]

Hello,

Thank you for sharing your work on simulating the chaotic action of a pendulum with magnets. It sounds like an interesting project.

To answer your question, let's first discuss the concept of degrees of freedom. In physics, degrees of freedom refer to the number of independent parameters that define the state of a system. In the case of your pendulum, there are three components to the angle vector - the x, y, and z components. Each of these components represents a different axis around which the pendulum can rotate.

Now, let's consider the forces acting on the pendulum. The pendulum is subjected to the force of gravity, which always acts in the vertical direction. This means that the pendulum can only rotate around the vertical axis. Therefore, the x and y components of the angle vector are not relevant in this case.

By forcing one of the components of the angle vector to be zero, you are essentially restricting the pendulum's motion to only one degree of freedom - rotation around the vertical axis. This simplifies the simulation and makes it more accurate since it is more closely aligned with the real-world scenario.

Using all three components of the angle vector may still produce accurate results, but it would introduce unnecessary complexity and may not accurately represent the physical system.

In conclusion, forcing one of the components of the angle vector to be zero is necessary in this case because it aligns with the physical reality of the pendulum's motion. I hope this explanation helps clarify things for you. Keep up the good work on your project!

 

[charng]

First of all, congratulations on successfully simulating the chaotic behavior of a pendulum with magnets! It sounds like you have put a lot of thought and effort into your program.

To address your question about forcing one of the components of the angle vector to be zero, I would need more information about your simulation and the specific equations you are using. However, I can offer some general insights that may help explain why this is necessary.

Firstly, when modeling a physical system, it is important to consider all the relevant forces and factors that affect its behavior. In this case, the pendulum is subject to the force of gravity and the magnetic force from the nearby magnets. The angle of the pendulum is a crucial factor in determining the direction and magnitude of these forces.

By forcing one component of the angle vector to be zero, you are essentially restricting the pendulum's movement to a specific plane. This simplifies the calculations and allows you to focus on the effects of the remaining two components. Without this restriction, the pendulum's behavior may become more complex and difficult to accurately simulate.

Additionally, using all three components of the angle vector may provide a more detailed and accurate representation of the pendulum's movement. It allows for the consideration of any potential rotations around different axes, which may be important in capturing the full chaotic behavior of the system.

In summary, forcing one component of the angle vector to be zero may simplify the simulation and make it more manageable, but using all three components may provide a more comprehensive and accurate representation of the pendulum's behavior. I would suggest experimenting with different combinations and seeing how they affect the results of your simulation. Keep up the good work!