质量驱动的Duffing型振子的非线性动力学：Lagrange方程与Newton方程的等价性
On the nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator: Lagrange and Newton equations' equivalence
摘要：
使用广义坐标和适当的可逆坐标变换，我们证明Bagchi等人16使用的欧拉-拉格朗日方程明显违反了汉密尔顿原理。我们还表明，牛顿的运动方程，他们使用的是不是在一个形式，满足动态的位置相关的质量（PDM）设置。Euler-Lagrange方程和Newton方程之间的等价性现在通过适当的可逆坐标变换和引入一个新的PDM副产反作用型力来证明和记录。PDM的总机械能显示为保守的（即，dE/dt=0，与Bagchi等人不同。的16个观察值）。
英文摘要：
Using a generalized coordinate along with a proper invertible coordinate transformation, we show that the Euler-Lagrange equation used by Bagchi et al. 16 is in clear violation of the Hamilton's principle. We also show that Newton's equation of motion they have used is not in a form that satisfies the dynamics of position-dependent mass (PDM) settings.. The equivalence between Euler-Lagrange's and Newton's equations is now proved and documented through the proper invertible coordinate transformation and the introduction of a new PDM byproducted reaction-type force. The total mechanical energy for the PDM is shown to be conservative (i.e., dE/dt=0, unlike Bagchi et al.'s 16 observation).
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