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 .

~~~

If

then

— 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

.

Eq. (1.133):

Eq. (1.144):

,

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

.

.

2023.04.07 Friday (c) All rights reserved by ACHK