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anirocks11
In Lagrangian mechanics, if the Lagrangian is not a function of one of the generalised coordinate, then it is called a cyclic coordinate. Why is it called such? What is the significance of the term 'cyclic'?
anirocks11 said:In Lagrangian mechanics, if the Lagrangian is not a function of one of the generalised coordinate, then it is called a cyclic coordinate. Why is it called such? What is the significance of the term 'cyclic'?
Cyclic coordinates are named as such because they describe a system that has periodic motion or behavior. This means that the coordinates repeat themselves after a certain amount of time or distance, just like a cycle.
Cyclic coordinates are important in science because they help us understand and predict the behavior of systems that have periodic motion. This can include everything from celestial bodies to chemical reactions.
Cyclic coordinates are different from other types of coordinates because they are independent of one another and do not affect the overall behavior of the system. This means that they can be treated separately and simplifies the analysis of the system.
No, cyclic coordinates can only be used to describe systems that have periodic behavior. They are not applicable to systems that do not exhibit this type of motion.
Yes, there are many real-life examples of cyclic coordinates. Some common examples include the Earth's orbit around the Sun, the rotation of a bicycle wheel, and the swinging of a pendulum.