Abstract
A complex representation of the equations of motion of the Foucault's pendulum is considered and the inverse problem is solved to derive an indirect analytic representation. Both real LR(i) and imaginary LI(i) parts of the derived complex valued Lagrangian are found to reproduce the equations of motion via the Euler-Lagrange equations. The expressions for LR(i) and LI(i) are not connected by a gauge term thereby forming a set of inequivalent Lagrangians. In an appropriate limit LI(i) is found to reproduce the Lagrangian obtained by implementing the usual Coriolis theorem while in some other limit LR(i) and LI(i) give the indirect and the direct analytic representations for a set of two uncoupled harmonic oscillators.
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