Spacelike Lines with Special Trajectories and Invariant Axodes
The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/5/1087 |
| _version_ | 1797598245787009024 |
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| author | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_facet | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_sort | Areej A. Almoneef |
| collection | DOAJ |
| description | The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fields such as robotics and mechanical engineering. |
| first_indexed | 2024-03-11T03:16:37Z |
| format | Article |
| id | doaj.art-ac1c74ad011c4dd89d30ef66cd652445 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:37Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ac1c74ad011c4dd89d30ef66cd6524452023-11-18T03:30:45ZengMDPI AGSymmetry2073-89942023-05-01155108710.3390/sym15051087Spacelike Lines with Special Trajectories and Invariant AxodesAreej A. Almoneef0Rashad A. Abdel-Baky1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, EgyptThe association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fields such as robotics and mechanical engineering.https://www.mdpi.com/2073-8994/15/5/1087timelike axodesEuler–Savary equationDisteli-axis |
| spellingShingle | Areej A. Almoneef Rashad A. Abdel-Baky Spacelike Lines with Special Trajectories and Invariant Axodes Symmetry timelike axodes Euler–Savary equation Disteli-axis |
| title | Spacelike Lines with Special Trajectories and Invariant Axodes |
| title_full | Spacelike Lines with Special Trajectories and Invariant Axodes |
| title_fullStr | Spacelike Lines with Special Trajectories and Invariant Axodes |
| title_full_unstemmed | Spacelike Lines with Special Trajectories and Invariant Axodes |
| title_short | Spacelike Lines with Special Trajectories and Invariant Axodes |
| title_sort | spacelike lines with special trajectories and invariant axodes |
| topic | timelike axodes Euler–Savary equation Disteli-axis |
| url | https://www.mdpi.com/2073-8994/15/5/1087 |
| work_keys_str_mv | AT areejaalmoneef spacelikelineswithspecialtrajectoriesandinvariantaxodes AT rashadaabdelbaky spacelikelineswithspecialtrajectoriesandinvariantaxodes |