Usually in a classical mechanics class, the Lagrangians are time independent and hence have a conserved energy. Occasionally, a teacher writes down a contrived example with a simple time dependence but usually without trying very hard (if at all) to connect the example to the physical world we live in. I was wondering if someone knows a good physically relevant example of a time dependent Lagrangian. I would be especially interested in an example which is useful for modeling a familiar physical phenomenon.
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