Abstract
The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t −4/3 q 1/2.
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Alexander von Humboldt-Stiftung Fellow, on leave from the Department of Physics, Ramjas College (University of Delhi), Delhi 110 007, India.
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Kaushal, R.S. Third and fourth order invariants for one-dimensional time-dependent classical systems. Pramana - J Phys 24, 663–672 (1985). https://doi.org/10.1007/BF02846785
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DOI: https://doi.org/10.1007/BF02846785