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Derives Jacobi’s integral of motion for a particle in rotating potentials, highlighting classical mechanics applications.
We consider the derivation of Jacobi’s integral of motion for a particle moving in a uniformly rotating potential, as a simple illustrative application of Noether’s theorem. We also provide some examples of Jacobi’s integral. In particular, we show that some elementary problems usually discussed in texts of classical mechanics can be interpreted in terms of Jacobi’s integral.
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Giordano et al. (1998) studied this question.
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