文摘
The motion of a physical system can generally be described by multiple coordinate representations, which obey nonlinear equations of motion and are related by nonlinear transformations. Here, the equivalence of the linearized equations of motion, related through the linearized transformations, is demonstrated. This equivalence is used to develop a calibrated linearized solution for highly nonlinear coordinates that can provide greater accuracy than the traditional linearized solution. The calibration process computes an alternate initial condition which is propagated with the linearized equations, instead of the true initial condition. Additionally, the inverse of the calibration process is used to develop a decalibrated solution, which is a nonlinear analytic approximation.