Some laws of motion of a system of many particles
Abstract
An opticalmechanical analog is used to determine the spatial distribution of a system of a large number of particles, and in particular, a possible periodic distribution along an axis in onedimensional motion. It is assumed that there are several sources of material particle input, and at some distance from the sources particle mixing takes place, such that the particles fill nearly continuously a part of space. Motion of the system is described by the characteristic Jacobi function. The relationship between the Jacobi function and the Fresnel wave equation is studied. Periodic distribution of velocities and density is observed in a onedimensional scheme at given input velocity by neglecting resistive forces, mass change, and part of interaction forces.
 Publication:

Problems of Analytical Mechanics and Stability and Control Theories
 Pub Date:
 1975
 Bibcode:
 1975pams.book..160K
 Keywords:

 Dynamic Characteristics;
 Many Body Problem;
 Particle Density (Concentration);
 Spatial Distribution;
 Analogies;
 Jacobi Integral;
 Partial Differential Equations;
 Wave Equations;
 Physics (General)