I am taking Analytical Mechanics and while reading Goldstein's and LL something bothered me: can I say that a degree of freedom is an independent (generalized) coordinate?
What bothers me is that we say that the number of degrees of freedom is the number of independent quantities necessary to determine the position of the system - we say what the number of degrees of freedom is, not what is a degree of freedom.
For example, in LL, page 1:
"To define the position of a system of $N$ particles in space, it is necessary to specify $N$ radius vectors, i.e. $3N$ coordinates. The number of independent quantities that must be specified in order to define uniquely the position of any system is called the number of degrees of freedom".
I am not sure that "my" definition above is correct, as it seems redundant to define generalized coordinates and then say that a degree of freedom is an independent coordinate.
Could you give a formal and rigorous definition?
