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MOMENTS OF A FLAT PLATE RELATIVE TO A STRAIGHT LINE AND SOME QUESTIONS OF SYMMETRY

DOI: 10.46573/2658-7459-2021-78-84

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Authors

Al.An. Shum , A.M. Vetoshkin , An.Al. Shum

Abstract

The concept of n-th order moment of a flat plate relative to a given straight line is considered. A straight line is declared to be a line of n-symmetry if the moments of the n-th order of two sub-plates into which the original plate is divided by this straight line are the same. In this case, the lines of 0-symmetry turn out to be half-mass lines, and the lines of 1-symmetry – lines of equilibrium. The lemma proved earlier for half-mass lines and equilibrium lines can be carried over to the more general case of lines of n-symmetry.

Keywords

symmetry, c-symmetry, s-symmetry, center of symmetry, half-mass line, equilibrium line, density function, mass, center of mass, electric machine.