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>An Argument Against Augmenting the Lagrangean for Nonholonomic Systems
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An Argument Against Augmenting the Lagrangean for Nonholonomic Systems
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机译:反对为非完整系统扩大Lagrangean的争论
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摘要
Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.
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机译:在端对端激活f 1 Sub>(00)的“ k”个“最小化区域”结果参数 +1 Sup> m k Sub>中生成的方法 min Sub>→ +1 Sup> m k Sub>用于根据三元数系统的f(+ 1,0,-1)结构的算术公理进行转换模拟信号的参数“«-/ +»[m j Sub>] f(+/-)--”互补代码“转换为条件最小化位置信号的结构模拟信号±< / Sup> [m j Sub>] f усл Sub>(+/-) min Sub>及其实现的功能结构(俄罗斯逻辑版本)