Abstract
We extend the results obtained in Sarlet and Prince (2010 J. Phys. A: Math. Theor. 43 445204) about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system.
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