1208.2300 (Sara Cruz y Cruz et al.)

Lagrange Equations And Spectrum Generating Algebras Of Mechanical
Systems With Position-Dependent Mass    [PDF]

Sara Cruz y Cruz, Oscar Rosas-Ortiz

We discuss on the construction of the Lagrangian for a classical system with mass varying explicitly with position. The conventional Lagrange equations cannot be directly applied to this system because there is a non-conservative force quadratic in the velocity which is associated to the variable mass. We construct a Hamiltonian for this system and find the modifications which are required on the Euler-Lagrange and Hamilton's equations in order to reproduce the appropriate Newton's dynamical law. A canonical transformation is found to map the variable mass equations to the ones of a constant mass. The time-dependent first integrals of motion are found in terms of the factorization of the Hamiltonian. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the Poschl-Teller form which seem to be new. The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian.

View original: http://arxiv.org/abs/1208.2300