Generalization of the Lagrange Equations Formalism, for Motions with Respect to Non-Inertial Reference Frames

Abstract

The paper presents an original generalization of the Lagrange equations of the second kind, for motions with respect to reference frames in arbitrary motions. The traditional form of the equations is modified by adding certain supplementary terms. Calculation methods are presented for these terms and some conclusions useful in practical applications are drawn. For validation, the new formalism is illustrated on the application of the Foucault pendulum. The results are in full agreement with those obtained by traditional methods. The formalism can be used to determine the motions of various mechanical systems, with respect to large size movable bodies (such as planets or orbital stations), that are not influenced by the relative motion of the studied parts.