Manual,
An introduction to Lagrangian and Hamiltonian mechanics
(2016)
Abstract
Newtonian mechanics took the Apollo astronauts to the moon. It also took
the voyager spacecraft to the far reaches of the solar system. However Newto-
nian mechanics is a consequence of a more general scheme. One that brought
us quantum mechanics, and thus the digital age. Indeed it has pointed us
beyond that as well. The scheme is Lagrangian and Hamiltonian mechanics.
Its original prescription rested on two principles. First that we should try to
express the state of the mechanical system using the minimum representa-
tion possible and which re ects the fact that the physics of the problem is
coordinate-invariant. Second, a mechanical system tries to optimize its
action
from one split second to the next. These notes are intended as an elementary
introduction into these ideas and the basic prescription of Lagrangian and
Hamiltonian mechanics. The only physical principles we require the reader
to know are: (i) Newton's three laws; (ii) that the kinetic energy of a particle
is a half its mass times the magnitude of its velocity squared; and (iii) that
work/energy is equal to the force applied times the distance moved in the
direction of the force.
