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- W4385494649 abstract "We revisit the notion of parametrization invariance while introducing certain weakened notions of invariance in the calculus of variations. In this work, we employ a straightforward approach in the classical setting and mostly restrict attention to functionals on one-dimensional domains. We establish a connection between parametrization invariant functionals and functionals embodying a weaker notion of invariance of their Lagrangian; we term this notion as [Formula: see text]- Lagrangian analogous to the well-known idea of null Lagrangian. However, the Euler–Lagrange operator of a [Formula: see text]-Lagrangian vanishes only along the tangential direction in the configuration space. On one-dimensional domain and for first- and second-order theories, we show that functional described by such a Lagrangian is necessarily a parametrization invariant functional modulo null Lagrangian. Keeping the motivation for partial differential equations, we also introduce and explore the notion of [Formula: see text]- Lagrangian, with an invariance complementary to the case of [Formula: see text]- Lagrangian, whose Euler–Lagrange operator vanishes along normal directions. We find that in a one-dimensional setting, every [Formula: see text]-Lagrangian is simply a null Lagrangian." @default.
- W4385494649 created "2023-08-03" @default.
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- W4385494649 date "2023-08-02" @default.
- W4385494649 modified "2023-09-27" @default.
- W4385494649 title "Generalizing parametrization invariance in the calculus of variations" @default.
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- W4385494649 doi "https://doi.org/10.1177/10812865231181890" @default.
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