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Non-autonomous mechanics

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Non-autonomous mechanics describe non-relativistic mechanical systems subject to time-dependent transformations. In particular, this is the case of mechanical systems whose Lagrangians and Hamiltonians depend on the time. The configuration space of non-autonomous mechanics is a fiber bundle Q → R {\displaystyle Q\to \mathbb {R} } over the time axis R {\displaystyle \mathbb {R} } coordinated by ( t , q i ) {\displaystyle (t,q^{i})} .