Legendre Transformation and Its Applications

Authors

  • Natalia Pavlova Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia; RUDN University, Moscow, Russia
  • Alexey Remizov Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia

DOI:

https://doi.org/10.25728/assa.2025.2025.1.2042

Keywords:

Legendre transformation, duality, contact transformation, contact structure, pedal curve, singular point, Clairaut equation

Abstract

We present the Legendre transformation in a geometric way based on the procedure of the Legendrian lift. This approach allows us to understand some interesting properties of it, in particular, the reason for the appearance of singularities of dual curves. Also we consider application of the Legendre transformation to the Clairaut differential equation. Finally, we say a few words class of contact transformations and present an infinite group of contact transformations different from the Legendre transformation.

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Published

2025-08-24

Issue

Vol. 2025 No. 1 (2025): Advances in Systems Science and Applications

Section

Articles

How to Cite

Legendre Transformation and Its Applications. (2025). Advances in Systems Science and Applications, 2025(1), 44-54. https://doi.org/10.25728/assa.2025.2025.1.2042