Understanding Generalized Coordinates in Goldstein's Classical Mechanics

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Generalized coordinates encompass any coordinate system, including Cartesian, polar, and spherical coordinates. They allow for flexibility in problem-solving, particularly when using Lagrange's equations. While polar and spherical coordinates can be classified as generalized coordinates for a single particle's position, the term "generalized coordinates" is broader and includes all types of coordinate systems. Thus, even Cartesian coordinates qualify as generalized coordinates. Understanding this concept is crucial for effectively applying Goldstein's classical mechanics.
radou
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I have just started to read Goldstein's classical mechanics, and he got me a bit confused: is it correct to think of polar and spherical coordinates as of generalized coordinates? the way I got it, every coordinate system different from the standard cartesian-one is a set of generalized coordinates...?
 
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No. Think about the 1D movement along the "x" axis. Which is the generalized coordinate...?

Daniel.
 
Generalized coordinates refer to any coordinate system. i.e. a statement about generalized coordinates holds for cartesian, spherical, cylindrical, etc. coordinate systems. In particular, one is free to choose any convenient coordinate system for a problem and solve the problem using Lagrange's equations for that coordinate system.
 
radou said:
I have just started to read Goldstein's classical mechanics, and he got me a bit confused: is it correct to think of polar and spherical coordinates as of generalized coordinates?

Yes, polar and spherical coordinates are generalized coordiantes for the position of a single particle. But general coordinates are a lot moe general. And cartesian coordinates are, technically at least, also "general coordinates".

Carl
 
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