This chapter is devoted to the methods of classical mechanics that allow the study of the motion of gas, liquid and solid particles as a system of interactive, dimensionless mass points. The classical dynamic equations of motion are valid for slow and heavy particles, with typical velocities v c, c being the speed of light, and masses m m e , m e being the electron mass. Therefore, only slow motion (slower than thermal vibrations) of atoms, ions and molecules can be considered, and the internal electronic structure is ignored. The atoms and molecules exert internal forces on each other that are determined by instantaneous values of the total potential energy of the system. The potential energy is typically considered only as a function of the system spatial configuration and is described by means of interatomic potentials. These potentials are considered as known input information; they are either found experimentally or are computed by averaging over the motion of the valence electrons in the ion's Coulomb field by means of quantum ab initio methods. During the course of the system's dynamics, the interatomic potentials are not perturbed by possible changes in the internal electronic states of the simulated particles.
Analytical solutions of the equations of particle dynamics are possible only for a limited set of interesting problems and only for systems with a small number of degrees of freedom. Numerical methods of solving the classical equations of motion for multiparticle systems with known interatomic potentials are collectively referred to as molecular dynamics (MD). MD is regarded as a major practical application of the classical particle dynamics. The subsequent computer postprocessing and visualization of the results accomplished in a dynamic manner are called the molecular dynamics simulation.
2.1 Mechanics of a System of Particles
Classical dynamics studies the motion of mass points (ideal dimensionless particles) due to known forces exerted on them. These forces serve as qualitative characteristics of the interaction of particles with each other (internal forces) and with exterior bodies (external forces). The general task of dynamics consists in solving for the positions (trajectories) of all particles in a given mechanical system over the course of time. In principle, such a solution Nano Mechanics and Materials: Theory, Multiscale Methods and Applications W.