Classical mechanics is that part of classical physics dealing with the physics of point particle?s and rigid bodies; compare classical field theory, which deals with the physics of physical fields.
Zoran: I disagree. Classical mechanics is classical mechanics of anything: point particles, rigid bodies (the latter I already included), infinite systems (mechanics of strings, membranes, springs, elastic media, classical fields). It includes statics, not only dynamics. The standard textbooks like Goldstein take it exactly in that generality.
One could even count the simplified beginning part of the specialized branches like aerodynamics and hydrodynamics (ideal liquids for example), which are usually studied in separate courses and which in full formulation are not just mechanical systems, as the thermodynamics also affects the dynamics. There are also mechanical models of dissipative systems, where the dissipative part is taken only phenomenologically, e.g. as friction terms. Hydrodynamics can also be considered as a part of rheology.
Toby: I take your point that ‘dynamics’ was not the right word. But do you draw any distinction between ‘classical mechanics’ and ‘classical physics’? Conversely, what word would you use to restrict attention to particles instead of fields, if not ‘mechanics’? (Incidentally, I would take point particles as possibly spinning, although I agree that I should not assume that the particle are points anyway.)
Zoran: you see, in classical mechanics you express all you have by attaching mass, position, velocity etc. to the parfts of mechanical systems. Not all classical physics belongs to this kind of description. The thermodynamical quantities may influence the motion of the systemm, but their description is out of the frame of classical mechanics. If you study liquids you have to take into account both the classical mechanics of the liquid continuum but also variations of its temperature, entropy and so on, which are not expressable within the variables of mechanics. Formally speaking of course, the thermodynamics has very similar formal structure as mechanics, for example Gibbs and Helmholtz free energies and enthalpy are like Lagrangean, the quantities which are extremized when certain theremodynamical quantities are kept constant. To answer the terminological question, there is a classical mechanics of point particles and it is called classical mechanics of point particles, there is also cm of fields and cm of rigid bodies.
Toby: So ‘mechanics’ for you means ‹not taking into account thermal physics›? That's not the way that I learned it! But I admit that I do not have a slick phrase for that (any more than you have a slick phrase for ‹mechanics of point particles›), so I will try to ascertain how the term is usually used and defer to that.
Nondissipative systems with finitely many degrees of freedom may be described geometrically using symplectic manifolds, or more generally Poisson manifolds; the later may also sometimes appear as reductions of the systems with infinitely many degrees of freedom.
Classical mechanics of a system of point particles and rigid bodies is usually divided into statics, kinematics and dynamics. Statics studies the balance of forces in a system which does not move, or in a stationary flow. Kinematics studies the relation between position, velocity and acceleration of bodies in a mechanical system, without reference to the causes of motion. Dynamics studies motion with reference to the causes of motion and interaction between bodies and its manifestation via (quantified) forces, energy and mass assigned to bodies in motion and interaction.
Mathematically, the theoretical classical mechanics is a rather special case of the theory of dynamical system?s which studies general spacially-parametrized systems in a (discrete or continuous) time evolution.
I removed ‘non-statics’ here, since one can study statics within dynamics if one wants to (by searching for static solutions). —Toby
But the thing is that in the subject of the dynamical systems you have some equations of motion, or some Hamiltonian, you do not analyse forces between bodies, but rather abstract them into the laws of motion, so in some sense it is not entirely true that dynamical systems take into account the whole subject of classical mechanics. Once you abstract to the symplectic manifodl or phase space yes, but the orginal problem with pulleys, strings, spins, forces and frictions to name a few is never studied in dynamical systems community. But I am mainly OK with your formulation. zoran