Based on the localization features of physical objects in time and space, in the study of the laws of classical mechanics, movement begins with a very simple case.This event is the motion of a material point.Sketch idea of elementary particle analytical mechanics forms the background for the presentation of the basic laws of dynamics.
material point - an object that has an infinitesimal size and final weight.This idea meets notions of discrete nature of matter.Previously, physicists have tried to define it as a set of elementary particles that are able to move.In this regard, the material point in its dynamics has become just necessary for the theoretical constructs tool.
dynamics of the object based on the inertial principle.According to him, the material point, not under the influence of external forces, maintains its state of rest (or displacement) over time.This regulation is carried out strictly enough.
In accordance with the principle of inertia, mass point (free) moves uniformly in a straight line.Considering the special case in which the velocity is zero, it can be said that the object retains the rest.In this regard, it can be assumed that the influence of a certain force on the subject under consideration is to simply change its velocity.The simplest hypothesis is the assumption that the rate of change, which has a material point is directly proportional to the indicator force acting on it.Wherein the proportionality factor decreases with increasing inertia.
Natural is a characteristic of a material point by a coefficient of inertia - the masses.In this case, the main law of motion of the object may be formulated as follows: acceleration imparted at each time equal to the ratio of force that acts on an object to its mass.Statement of kinematics, thus precedes the presentation of the speakers.Mass, which describes the dynamics of the material point, is introduced a posteriori (from experience), while the presence of a trajectory position, acceleration, velocity may be a priori.
In this regard, the equation object dynamics argue that the product of the mass of the object to any of the components of its acceleration is equal to the corresponding component of the force acting on the object.Assuming that the force is a known function of time and coordinates, for the determination of the coordinates of a material point in accordance with the time produced by the three ordinary differential equations of second order in time.
In accordance with the well-known theorem of calculus course, a solution to this system of equations is uniquely defined by coordinates, as well as their first derivatives at some initial time period.In other words, when a certain position in terms of material and its velocity at a particular point can accurately determine the nature of its displacement in all future periods.
As a result, it is clear that the classical dynamics of the object is in absolute accordance with the principle of physical determinism.According to him, the upcoming state (status) of the material world can be predicted entirely in the presence of the parameters that define its position in some previous moment.
Due to the fact that the size of the material point is infinitesimal, its trajectory will be a line in three-dimensional space it occupies only one-dimensional continuum.In every part of the trajectory there is a certain value of the force, set to move to the next infinitesimal period of time.
