Integration of the Classical Action for the Quartic Oscillator in 1 + 1 Dimensions
, PP. 117-122 10.4236/am.2013.410A3014
Keywords: Action, Integral
In this paper, we derive an explicit form in terms of
end-point data in space-time for the classical action,
i. e. integration of the Lagrangian
along an extremal, for the nonlinear quartic oscillator evaluated on extremals.
[ 1] H. Goldstein, “Classical Mechanics,” Addison-Wesley Publishing Company, Reading, 1980.
[ 2] R. L. Anderson, “An Invertible Linearization Map for the Quartic Oscillator,” Journal of Mathematical Physics, Vol. 51, No. 12, 2010, Article ID: 122904.
[ 3] R. C. Santos, J. Santos and J. A. S. Lima, “HamiltonJacobi Approach for Power-Law Potentials,” Brazilian Journal of Physics, Vol. 36, No. 4A, 2006, pp. 12571261.
[ 4] R. L. Anderson, “Actions for a Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1 + 1 Dimensions,” arXiv.org:1204.0768.