Назад      Главная страница      Оглавление     Далее  

Abstract. A theoretical calculation is made of the total energy of the wave vortex in a vacuum, for the general case.

   The formula is derived in accordance with the laws of mechanics for a solid. It is more convenient to deploy the lok so that all the oscillations occur parallel to the vertical axis  Z , and the rotation of waves around this axis.  Such a choice is denoted as  W₀ .

(1-11)

   Further, for simplicity, the constant C_j, m and the time dependence are not considered, because in the process of voltage oscillations in the fixed-locus element the sum of the kinetic and potential energy does not change and is determined by the point at which cos (ωt + δ) = 1.

(1-12)

Where  W_x , W_y , W_z  are three components of the solution (1-2). Or with the choice of (1-11):

(1-13)

   Next, we need the strain tensor in the lok.

(1-14)

(1-15)

Definitions are introduced:

(1-16)

   Where  L₁  and  L₂ - Lame Gukuum coefficients (elasticity characteristics);  i,k = 1,2,3 - indices of variables.

   Volume element in spherical coordinates:
 

       dv = r²•sinθ•dr•dθ•dφ ;                                            (1-17)
 

(1-18)

Where  Ф - The functional factor, which takes into account the "stratification" of the solution. It is taken equal  (1/r)² . It is more convenient to proceed to a dimensionless variable.
  Please note that this is where the dimensionless coordinate appears q ! :
 

         q = k•r ;                                                            (1-19)
 

(1-20)

   Calculation of this formula is the most laborious place, if you work manually. The results are achieved using computer programs. A huge thanks to their developers.
    We expand the expression for the integral of the total energy (1-20):

(1-21*)

   The sign * is entered here so that there are no coincidences with subsequent chapters.
   Next we sequentially set the values  j = 1,2,3,…  m = 0,1,…,j . Then, according to equation (1-11), we choose  W₀ . After this, using the formula (1-13), we find the values of the quantities  W_r , W_θ , W_φ . After that, we substitute these values into the integral expression (1-21 *) and calculate these integrals.
    For such formulas it is possible to compile a computer algorithm. For each pair  (j,m)  their numerical coefficients in (1-21 *) will be obtained. Within a few days, we managed to calculate a certain array of integrals on the computer. And these results deserve attention. It turned out that in all tested combinations of integer parameters the total energy of the lok depends only on the sum of the Lamé elasticity characteristics for Gukuum  L₁  и  L₂ . Change only ahead of the standing coefficients.

   Table of energy levels.
   There is a serious assumption that this is the table of all particles of the universe. In each cell it is necessary to set the values of the analogous coefficient for the angular momentum, the wave number  k , as well as the effective particle size  D .

(1-36*)

    Spin of lok (j,m). (The derivation of this formula is given in the following chapters).

(1-37*) 

j =0,1,2,…;   m =0,1,2,… . K_j,m - Some numerical coefficients that are obtained in the process of integrating formulas (1-33 *).
    Below is the beginning of this infinite, both in length and in width of the table. For momentum moments in the absence of time, only a few coefficients have been calculated so far. It is established that for even j the angular momentum is zero.
    Important: in the formula along with the amount  (L₁+L₂)  entered the constant  C . This constant is different for different loks. Therefore, the table of coefficients K_j,m, may require improvement. To introduce a physical meaning, it is necessary to take into account the real masses of particles.

Table 1.

    Note. The values  k = ω/c  for each pair  (j,m)  various. Growth in tabular coefficients with growth  (j,m)  does not indicate that the masses of loks are growing. All solves the constant  C  in the solution, and the wave number k.