In this paper Gauss’ principle of least constraint is used to obtain approximate solutions of conservative and nonconservative dynamical systems. The main feature of the method is that every particular problem is reduced to an algebraic problem of minimizing a quadratic form with respect to the physical components of the acceleration vector of the system, or with respect to the components of a generalized force. The method is illustrated by solving several problems. The method is equally applicable to ordinary as well as partial differential equations. A brief criticism of the least-squares method, as a method of solving differential equations, is given.

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