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Non-integrability of the degenerate cases of the Swinging Atwood's Machine using higher order variational equations

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  • Non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations (VEk), 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).
    Mathematics Subject Classification: Primary: 37J30, 70H07; Secondary: 34M35.


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