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This book offers a new method for the formalized construction of approximate mathematical models of dynamic systems described by ordinary differential equations (ODE). The models illustrate the separated components of the motion of initial systems. This procedure, termed by Kline as "fractional analysis", consists of two stages. First, appropriate small parameters are introduced into initial equations by normalization, and then appropriate methods of small parameter are used to obtain equations of the separated "fractions". As shown in the book, a wide range of problems can be investigated in this way. The author suggests a new means of introducing small parameters, and surveys existing various methods of small parameter such as Poincare method, the method of averaging, and the method of boundary-layer expansions. Their applicability is discussed. The book is application oriented, so proofs of theorems are omitted and mathematical formulations are simplified. Emphasis is on approximate modeling in mechanics, the theory of gyroscopic transport, and robotic systems.
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