Abstract
The approximate Noether theorem and its inverse theorem for the nonlinear dynamical systems with approximate exponential Lagrangian and approximate power-law Lagrangian are investigated. For each case, the approximate differential equations of motion for the nonlinear dynamical systems with approximate nonstandard Lagrangian are established, the generalized Noether identities are given. The relationship between the approximate Noether symmetries and approximate conserved quantities for the system with approximate nonstandard Lagrangian are established, and the approximate Noether theorems and their inverse theorems are obtained. Two examples are given to illustrate the application of the results.
Published Version
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