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The aim of this paper is to geometrize time-dependent Lagrangian mechanics in a way that the framework of second-order tangent bundles plays an essential role. To this end, we first introduce the concepts of time-dependent connections and time-dependent semisprays on a manifold M and their induced vector bundle structures on the second-order time-dependent tangent bundle $$\mathbb {R}\times T^2M$$ R × T 2 M . Then we turn our attention to regular time-dependent Lagrangians and their interaction with $$\mathbb {R}\times T^2M$$ R × T 2 M in different situations such as mechanical systems with potential fields, external forces and holonomic constraints. Finally, we propose some examples to support our theory.
Mediterranean Journal of Mathematics – Springer Journals
Published: Jun 23, 2017
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