The Legendre transformation is a mathematical operation that transforms a function of one variable into another function, providing a way to switch between different representations of the same physical system, particularly in mechanics. This transformation is key in relating Lagrangian and Hamiltonian formulations, allowing one to express the Hamiltonian in terms of momenta instead of velocities, which facilitates the study of dynamical systems.
congrats on reading the definition of Legendre Transformation. now let's actually learn it.