%0 Journal Article
%T Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
%A Sara Cruz y Cruz
%A Oscar Rosas-Ortiz
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%X We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. 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 P schl-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.
%K P schl-Teller potentials
%K dissipative dynamical systems
%K Poisson algebras
%K classical generating algebras
%K factorization method
%K position-dependent mass
%U http://dx.doi.org/10.3842/SIGMA.2013.004