A route to Routh—the parametric problem.
|Original title:||A route to Routh—the parametric problem.|
|Type:||Article in Periodical|
|Keywords:||Calculus of variations; Routh reduction; Poincare-Cartan form|
There is a well known principle in classical mechanic stating that a variational problem independent of a space variable $w$ (so called cyclic variable), but dependent on the velocity $w'$ can be expressed without both $w$ and $w'$. This is the Routh reduction principle. We develop a geometrical approach to the problem and deal with general first order variational integrals admitting a Lie symmetry group of point transformations.