Can equations of motion be of order higher than two?
The differential equation governing the time evolution of the position a point particle, known
as Newton's second law, is second order in time. Even after a lot of progress in our
understanding of the physical world, no physical system has ever been observed whose
dynamical variable evolves in time, in accordance with a higher-order differential equation.
This is not merely a coincidence, and there is a deeper, more fundamental reason to this.
Ostrogradsky's theorem is a strong no-go theorem that imposes a strong restriction on the
types of physical systems that can exist. The theorem states that the Hamiltonian of a system
that does depend on more than two initial-value pieces of information is usually not bounded from
below, and this is detrimental to the existence of the system. The aim of this project is to
understand Ostrogradsky's result in its spirit. The theory of classical mechanics is first learnt
in its Lagrangian and Hamiltonian formulations. Thereafter, Ostrogradsky's theorem is studied
and applied to general physical system which can possibly have a higher order equation of
Keywords: Lagrangian, Hamiltonian, Cannonical Co-ordinates, Equations of Motion