
105Lagrangian Formulation of Mechanics
© 2010 Taylor & Francis Group, LLC
From this, it follows that
P
i
= α
i
, i = 1, 2,…, n (4.32)
where the α
i
are constants evaluated from the initial conditions. They are called the rst integrals
of motion. We now nd a general conservation theorem: The generalized momentum conjugate
to a cyclic coordinate is conserved during the motion. This conservation theorem for generalized
momentum is more general than the conservation theorems for linear momentum and angular
momentum. In fact, the latter two conservation theorems are contained in the general conservation
theorem. For example, if q
1
does not appear in ...