ABSTRACT
A typical approach to the use of properties of symmetry is a dimensional analysis of the quantities included in the model. The part of characteristics of objects is measured in certain units with direct (mechanical, physical,
economic, etc.) * content. For example, the mass in grams, temperature in Kelvin degrees, national gross product in roubles. Such quantities are called dimensional, their numerical value depends on a choice of units of measure. Among them are distinguished the quantities with independent (basic) di mension, or dimension independent ones. For example, if for the description of a mechanical phenomenon the CGS system of units (centimeter, gram, second) is used, then the dimensions of length x, mass m and time t are independent and are not expressed through each other. On the contrary, the dimension of kinetic energy E = mv2 /2 is determined through the dimen sions of the basic quantities via the formula [E] = [ra][x]2[t]~2 = g • c2 • s“2, called the dimension formula (here v = dx/d t , the symbol [/] denotes the dimension of quantity / ) . Such quantities are called dimension dependent Recall that the phenomena and processes can be described also by dimensionless variables, say, by the ratio of the length of water carrier layer to its width, power index in a formula defining the dependence of the coefficient of thermal conductivity from temperature, annual bank percentage, etc.
