NON-INTEGRABILITY OF THE DEGENERATE CASES OF THE SWINGING ATWOOD'S MACHINE USING HIGHER ORDER VARIATIONAL EQUATIONS

摘要

Non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations (VEκ), are applied to prove the non-integrability of the Swinging Atwood's Machine for values of the parameter which can not be decided using first order variational equations (VE1).