Part I of this paper deals with relationships between integrals of a set of nonlinear differential equations and integrals of equations obtained from such a set by a process of linearization. The terms “total linearization,” “reduction,” and “partial linearization” are introduced, a theorem is stated and proved in connection with each of these, and the use of each theorem is illustrated by means of an example. In Part II, the theorems are applied to differential equations of motion of mechanical systems.

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