Structure and Interpretation of Classical Mechanics

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**e**. Make a Lagrangian () for the system described with the irredundant generalized coordinates , , and compute the Lagrange equations from this Lagrangian. They should be the same equations as you derived for the same coordinates in part **d**.

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Eq. 1.95:

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Eq. 1.97:

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71

Consider a function of, say, three arguments, and let be a function of two arguments satisfying .

Then .

The substitution of a value in an argument commutes with the taking of the partial derivative with respect to a different argument. In deriving the Lagrange equations for we can set and in the Lagrangian, but we cannot do this in deriving the Lagrange equations associated with , because we have to take derivatives with respect to those arguments.

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— Me@2021-11-24 09:58:31 PM

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