Structure and Interpretation of Classical Mechanics

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Show by direct calculation that the Lagrange equations for are satisfied if the Lagrange equations for are satisfied.

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Equation (1.69):

Equation (1.70):

Equation (1.71):

The Lagrange equation:

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Since it is just a coordinate transformation , has no explicitly dependent on . Similarly, if we consider the coordinate transformation , has no explicitly dependent on . So

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— Me@2020-12-28 04:03:24 PM

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2020.12.28 Monday (c) All rights reserved by ACHK