Generalized coordinates - Rotating pendulum

In summary, the conversation discusses the problem of a pendulum rotating about an axis. The question is raised as to why the angle of rotation about the axis is not considered a generalized coordinate in this scenario. The concept of Hamiltonian for the system is mentioned, as well as the uncertainty of including the term relative to the angle. The relationship between the angular velocity and constant rotation is also mentioned. The conversation concludes by considering that the orientation of the axis and the influence of gravity on the rotation may affect the cyclic nature of the coordinate and its time-derivative.
  • #1
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My question is kinda simple but it has been causing me some trouble for a while. In the problem of the pendulum rotating about an axis, why isn't the angle of rotation about the axis a generalized coordinate? The doubt appears when i try to write the hamiltonian for the system and i don't know if i include the term relative to that angle.
How that's related to the fact that the angular velocity is or not constant.
Thanks in advance.
( The problem considered is of a simple pendulum, but with its axis of oscillation rotating)
 
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  • #2
What is the orientation of that axis? If rotation around it is not influenced by gravity, the coordinate is cyclic (I think this is what you are looking for?) and its time-derivative is conserved.
 

1. What are generalized coordinates?

Generalized coordinates are a set of variables that describe the state of a system in terms of its degrees of freedom. They are typically chosen as independent variables that can uniquely specify the position and orientation of a system.

2. How are generalized coordinates different from regular coordinates?

Regular coordinates, such as Cartesian coordinates, describe the position of an object in terms of its distance from a fixed origin and along fixed axes. Generalized coordinates, on the other hand, are chosen to describe the position and orientation of a system in a more convenient and efficient way by taking into account the system's degrees of freedom.

3. What is a rotating pendulum?

A rotating pendulum is a physical system that consists of a pendulum attached to a rotating platform or frame. The pendulum swings back and forth under the influence of gravity, while the platform rotates around a fixed axis. This system is commonly used in physics experiments to study oscillations and rotational motion.

4. How are generalized coordinates used to describe a rotating pendulum?

In a rotating pendulum, the generalized coordinates would typically be the angle of rotation of the platform and the angle of the pendulum with respect to the vertical. These variables can uniquely describe the position and orientation of the pendulum in the rotating frame, making it easier to analyze the system's motion.

5. What are some applications of generalized coordinates in physics?

Generalized coordinates are commonly used in classical mechanics to describe the motion of systems with multiple degrees of freedom. They are also used in other fields such as quantum mechanics, fluid mechanics, and control theory to simplify mathematical calculations and make physical systems easier to understand and analyze.

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