Jacobi's last multiplier and symmetries for the Kepler problem plus a lineal story

摘要

We calculate the first integrals of the Kepler problem by the method of Jacobi's last multiplier using the symmetries for the equations of motion. Also we provide another example which shows that Jacobi's last multiplier together with Lie symmetries unveils many first integrals neither necessarily algebraic nor rational whereas other published methods may yield just one.