Suppose that I have a monatomic gas sample consisting of $N$ atoms (e.g., $N$ argon atoms); thus there are no vibrations or rotations. How many degrees of freedom does the system have?

• Does the system have $3N$ degrees of freedom? Each of the $N$ atoms can translate in $x$, $y$, and $z$, so $3N$ degrees of freedom seems reasonable. This seems to be supported by this website on molecular dynamics (MD), which states: "If there are $N$ atoms and $N_c$ internal constraints, then the number of degrees of freedom is $N_f = 3N - N_c$." It seems that a monatomic gas such as argon has no internal constraints, so the website seems to be suggesting $3N$ degrees of freedom.
• Does the system have $3N - 3$ degrees of freedom? Page 64 of Frenkel & Smit's Understanding Molecular Simulation: From Algorithms to Applications (2nd edition) seems to suggest that the system has $3N - 3$ degrees of freedom: "In practice, we would measure the total kinetic energy of the system and divide this by the number of degrees of freedom $N_f$ ($ = 3N - 3$ for a system of $N$ particles with fixed total momentum)." The only thing I am unsure of is whether a monatomic gas in general has fixed total momentum: probably not, unless there is solely center-of-mass motion.