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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See https://physics.stackexchange.com/q/311168/ – Ghoster Dec 04 '22 at 23:12
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- Take e.g. any Lagrangian and add an external source term. 2. E.g. consider the Lagrangian for a point charge in a time-dependent E&M background field.
– Qmechanic Dec 05 '22 at 03:07 -
Exercise 14 from chapter 2 of Goldstein feels contrived to me. Thank you for the example of the time-dependent E&M background field. – user2309840 Dec 07 '22 at 16:46