There are certain general principles or theorems in mechanics, such as Lagrange’s equations,
Hamilton’s principle, the principle of least work, and Gauss’ principle of least constraint, which
afford general solutions of certain types of problems. Such general principles have therefore the
advantage over ordinary methods in that once having found the general solution, any particular
problem may be solved by merely routine processes.
The general form of Lagrange’s equation for the generalized coordinates qi is given
as
where T is the kinetic energy and Qi is the generalized forces which is related to the system forces
through
The more common form, used when the forces for the dynamical system can be found from a scalar
potential function V , is
where L, the Lagrangian function (or, simply, Lagrangian), is the difference between the kinetic
and potential energy
