Abstract
Three traditional problems in accelerative mechanics are chosen to exemplify the manner of working by the proportionalities method. The formal construction of a proportionality is given and the form of the dimensional matrix of a monomial is discussed. Having chosen the dimensional in which the (n +1) term reduction of the variables of a dimensionally homogeneous set is to be explicitly dimensionally homogeneous, the variables of other dimensions may be systematically combined, as necessary, to leave only terms in the first chosen dimension and one other. The variables of the first dimension, together with the proportionalities formed in terms of the first dimension, can then be arranged to encompass the whole relationship between the variables of the set. This is done in a manner which readily allows formal display of all the choices in the nondimensionalization process of reduction from the (n +1) term equation to the n term nondimensional equation. The new method is considered shorter, and more precise, in leading to any one nondimensional solution, than the accepted methods. It can be amplified with little additional working to display the possibility of unfamiliar but valuable arrangements. The method runs parallel to a formal similitude method and thus appears to have greater physical significance than the traditional indicial equation methods of dimensional analysis.
Published Version
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