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Identifying Nonlinear Oscillators By An Energetic Functional In The Linear Space Of Temporal Boundary Functions, Chein-Shan Liu, Yung-Wei Chen, Jiang-Ren Chang

Journal of Marine Science and Technology

We resolve the inverse problems of a second-order nonlinear oscillator to recover time-dependent damping function and nonlinear restoring force, with the help of temporal boundary data measured at initial time and final time. By using these data, a sequence of temporal boundary functions of time is derived, which satisfy the measured temporal boundary conditions automatically, and are at least the fourth-order polynomials of time. All the temporal boundary functions and zero element constitute a linear space, and a new concept of energetic functional is introduced in the linear space, of which the energy is preserved for each energetic temporal boundary …