Basic Ideas and Conceptions of Classical Mechanics

The Newton movement equations describes motion of a mass point along a well-defined path which is defined by initial conditions and acceleration. The enrgy of particle moving in potential V(x) and having impulse p = mv (m: mass, v: velocity) is given by E = Ekin + V(x). Since Ekin = ½mv² and p = mv and therefore Ekin = p²/2m and altogether one can finally obtain the total energy equation:

E = p²/2m + V(x)

Since energy is conservative quantity, i.e. energy is time constant and impulse is given by p = m · dx/dt one can easily obtain the ordinary differential equation (ODE) relative to x the solution (or particle motion) of which can be obtained for all times knowing x(t = 0) and p(t = 0).

Example:
Harmonic oscillator; V(x) = ½ kx², E = p²/2m + ½ kx² Þ E = ½ m (dx/dt)² + ½ kx²
Having constant energy one can easily plot figures E = p²/2m + ½ kx² in (x,p)-phase space for different energies E1, E2,..:

The utter elegance in mass point movement (classical) description can be reached by using the Hamilton function H.
All equations of motion in classical mechanics are continuous functions.

In the case of gravitational interactions classical physics is especially successful and gives very good description of planets, moons and also artificial satellites motion. All the flights in space are calculated using classical mechanics. Its space application is limited only by few moments: for instance, Mercury perihelion rotation can be predicted with the accuracy of "only" 99,2%; the remainder requires improved theory - the General Relativity Theory. It's one of two utterly big theories in a world. The main features of another big theory "Quantum Mechanics" (Why quantum mechanics?) will be discussed a bit later, in this semester. Unification of the two theories is a great dream of humanity.

Another theory that brilliantly describes Maxwell equations is called electromagnetic theory. The Maxwell equations describe light as electromagnetic wave. If we move towards the Sun we would directly feel the heat produced by electromagnetic radiation of the Sun by our skin. It's essential for a wave that it is spread on the whole area contrary to mass point.

The first discontinuous functions can be met in spectroscopy:

1814 Fraunhofer studied lines in the Sun spectrum
1860 Bunsen and Kirchhoff developed the spectral analysis

The line spectrum is the atomic characteristic

1885 Balmer developed the empirical formula for the positions of emitted lines by hydrogen atoms that is as follows:

ν = RH(1/4−1/m²) m = 3, 4, 5......

RH: Rydberg constant = 3,29 · 1013 Hz

These measurements are not matched with the classical theory. Nevertheless, scientists were not care about these phenomena. The interests laid in the theoretical sphere of the Black Body Irradiation.