Lagrangian mechanics is a mathematical framework used to describe the motion of systems, while Hamiltonian mechanics is a mathematical framework used to describe the evolution of systems over time.
The minimum level of math required to learn Lagrangian and Hamiltonian mechanics is a strong understanding of calculus, including differential equations and multivariable calculus.
While a background in physics can be helpful, it is not necessary to learn Lagrangian and Hamiltonian mechanics. However, a strong understanding of mathematics is essential.
Some key math topics to focus on before learning Lagrangian and Hamiltonian mechanics include vector calculus, linear algebra, and differential equations. A strong foundation in these areas will make it easier to understand the concepts in Lagrangian and Hamiltonian mechanics.
While having a basic understanding of Newtonian mechanics can be helpful, it is not necessary to have prior knowledge of it before learning Lagrangian and Hamiltonian mechanics. However, some concepts from Newtonian mechanics will be built upon in Lagrangian and Hamiltonian mechanics, so it can be beneficial to have some familiarity with it.