A reformulation of → Newtonian mechanics
in which dynamical properties of the system are described in terms of
generalized variables.
In this approach the → generalized coordinates
and → generalized velocities
are treated as independent variables. Indeed applying Newton’s laws to complicated
problems can become a difficult task, especially if a description of
the motion is needed for systems that either move in a complicated manner, or other
coordinates than → Cartesian coordinates
are used, or even for systems that involve several objects. Lagrangian dynamics
encompasses Newton dynamics, and moreover leads to the concept of the
→ Hamiltonian of the system
and a process by means of which it can be calculated.
The Hamiltonian is a cornerstone in the field of
→ quantum mechanics.
See also: → Lagrangian; → dynamics.
