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I have seen both rk and qj both used to represent generalized coordinates in the Lagrange equations. Are these both the same things? Does it matter which you use?
Thanks!
Thanks!
Ok, but Wikipedia used both in the same article (even in the same equation). Are these just differing authors or is rk different?Orodruin said:No, what you are calling things are typically completely conventional. You could call energy R, mass x, and the speed of light T and you would have R = xT^2 - nobody would understand you if you did not specify what notation you were using though. The notation I have seen the most is to use q for generalized coordinates, but it really does not matter as long as you specify what you are doing and use a notation which is not inherently confusing.
But they use them in replace of qj in the Lagrange equations of the first kind.nasu said:If you mean this page
https://en.wikipedia.org/wiki/Lagrangian_mechanics
they don't use "r" for generalized coordinates but for the position vectors.
Generalized coordinates are a set of independent variables used to describe the configuration of a physical system. They are used in notation to simplify the mathematical representation of a system and make it easier to solve equations of motion.
Generalized coordinates are chosen to be independent of each other and can be chosen arbitrarily as long as they describe the configuration of the system. Other coordinate systems, such as Cartesian coordinates, are fixed and do not allow for arbitrary choices.
In theory, yes. However, the choice of generalized coordinates may not always be the most convenient or efficient way to describe a system. It is important to carefully consider the physical system and the constraints it poses when choosing generalized coordinates.
This conversion depends on the specific system and its constraints. In some cases, it may be straightforward, while in others it may require a more complex mathematical transformation. In general, it is best to consult resources or consult with an expert in the field for the appropriate conversion method.
A simple example is a pendulum, where the generalized coordinates could be the angle of the pendulum and the length of the string. Other examples include a double pendulum, a rigid body rotating in space, and a system of coupled oscillators.