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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00250 |
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| _version_ | 1866912458868785152 |
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| author | Ladeishchikov, E. A. Lokutsievskiy, L. V. Prilepin, N. V. |
| author_facet | Ladeishchikov, E. A. Lokutsievskiy, L. V. Prilepin, N. V. |
| contents | In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extremals are obtained in terms of convex trigonometric functions. In the sub-Lorentzian setting, the new trigonometric functions $\cosh_Ω$ and $\sinh_Ω$, developed here, prove especially useful; they generalize the classical $\cosh$ and $\sinh$ to the case of an unbounded convex set $Ω\subset\mathbb{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups Ladeishchikov, E. A. Lokutsievskiy, L. V. Prilepin, N. V. Optimization and Control In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extremals are obtained in terms of convex trigonometric functions. In the sub-Lorentzian setting, the new trigonometric functions $\cosh_Ω$ and $\sinh_Ω$, developed here, prove especially useful; they generalize the classical $\cosh$ and $\sinh$ to the case of an unbounded convex set $Ω\subset\mathbb{R}^2$. |
| title | Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.00250 |