Principle of transference - An extension to hyper-dual numbers

The algebra of hyper-dual numbers and hyper-dual vectors of order n, developed in this paper, follows the same rules as those of dual numbers and dual vectors. By showing that the basic formulae of vectors scalar and vector multiplication, hold for dual vectors of order n and that the basic trigonometric formulas hold for dual angles of order n, we concluded, that all formulae of vector algebra and trigonometric functions that are based on the above identities also hold for dual numbers of order n. This, as a result, extends Kotelnikov's "principle of transference" developed for dual numbers, to hyper-dual numbers of order n. (c) 2017 Elsevier Ltd. All rights reserved.