The Lagrangian and Hamiltonian formalisms in classical mechanics are based on the Newtonian concept of absolute time t which serves as the system evolution parameter in Hamilton’s Principle. This ap...The Lagrangian and Hamiltonian formalisms in classical mechanics are based on the Newtonian concept of absolute time t which serves as the system evolution parameter in Hamilton’s Principle. This approach violates the Special Theory of Relativity. The extended Lagrangian and Hamiltonian formalism is a parametric approach, pioneered by Lanczos, that renders it to a form that is compatible with the Special Theory of Relativity.
In classical mechanics we can describe the state of a system by specifying its Lagrangian as a function of the coordinates and their time rates of change.However, it is sometimes convenient to change ...In classical mechanics we can describe the state of a system by specifying its Lagrangian as a function of the coordinates and their time rates of change.However, it is sometimes convenient to change the basis of the description of the state of a system by defining a quantity called the hamiltonian H.
