Structure and Interpretation of Classical Mechanics

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An analogous result holds when the ‘s depend explicitly on time.

**a**. Show that in this case the kinetic energy contains terms that are linear in the generalized velocities.

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Eq. (1.141):

Eq. (1.142):

Eq. (1.133):

where is called the *generalized momentum*.

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where is the velocity selector. And has no velocity component?

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“… is a homogeneous function of the generalized velocities of degree 2.”

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What does the actually mean?

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Euler’s Homogeneous Function Theorem:

If

then

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So

Therefore,

— Me@2022.09.27 12:26:09 PM

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2022.09.27 Tuesday (c) All rights reserved by ACHK