Structure and Interpretation of Classical Mechanics
An analogous result holds when the ‘s depend explicitly on time.
c. Show, using Euler’s theorem, that the energy function is .
— Euler’s Homogeneous Function Theorem
This answer is not totally correct, since the generalized velocity, , should be a vector.
— Me@2022-11-01 08:58:52 AM
where is the momentum state function.
Since has no velocity dependence,
Since is a homogeneous function of the generalized velocities of degree 2, by Euler’s Homogeneous Function Theorem,
— Me@2023-04-06 12:49:49 PM
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