Recent content by Undoubtedly0

Thank you, wrobel. This was exactly what I was looking for. I have found it simple to show that there are at most ##2n## functionally independent constants-of-motion for a Hamiltonian of ##2n## freedoms.

In Principles of General Thermodynamics, Hatsopoulus and Keenan (p 442) make the following claim: What, however, would be some physical examples of such a system?

Thanks Khashishi. I have assumed that functional independence extends to more than two functions in the analogous way that linear independence does. That is, if ##E## and ##L## are constants of the motion, ##\{E,L,E^L\}## is not a functionally independent set. Said differently, what is the...

I am using Jose & Saletan's "Classical Dynamics", where they introduce a rather contrived Hamiltonian in the problem set: H(q_1,p_1,q_2,p_2) = q_1p_1-q_2p_2 - aq_1^2 + bq_2^2 where a and b are constants. This Hamiltonian has several constants-of-motion, including f = q1q2, as can be easily...

So if we take it to be the case that \frac{\partial \tau}{\partial x} = R(T)\frac{\partial T}{\partial x}, then what would be the value of \partial \tau/\partial x |_{x=c} ? \left.\frac{\partial \tau}{\partial x}\right|_{x=c} = R(T)|_{x=c} \cdot\left.\frac{\partial T}{\partial...

\theta is a dummy variable that stands for T = T(x,y), which I think means that R(\theta) = R(\theta(x,y)), correct?

Hi all. I am looking at the functions \tau(x,y), T(x,y), and R(T) related by \tau(x,y) = \int_{\pi}^{T(x,y)} R(\theta) d\theta . It seems that by Leibniz's integral rule \frac{\partial \tau}{\partial x} = \int_\pi^{T} \frac{\partial R}{\partial x} d\theta + R(T)\frac{\partial...

Thanks jtbell, this is something like what I was looking for.

Do there exist any "recreational physics" journals? Such as one that publishes simple, but interesting, applications of classical mechanics?

Hi all. What does it mean that a function in polar coordinates may not be a function in Cartesian coordinates? For example, r(\theta) = 1 + \sin\theta is a function because each \theta corresponds to a single value of r. However, in Cartesian coordinates, the graph of this function most...

Thanks mfb. Regarding our difference, I think your third term might be mistaken. If we hollow out the planet from 0 ≤ r < R/2, then the force due to gravity in the domain R/2 ≤ r ≤ R is F_G = \frac{Gm\frac{\rho}{3}}{r^2}\left[ \frac{4\pi}{3}r^3 -...

Here is a simple problem in classical gravitation. Consider a spherical planet of radius R, and let the radial coordinate r originate from the plant's center. If the density of the planet is ρ from 0 ≤ r < R/2 and ρ/3 from R/2 < r < R, then my work tells me that the maximum force due to...

Thanks Russ, you have answered my question. I imagine it is electric.

Hi all; an easy question for you. In the following picture, what is the ventilation box in the corner near the floor? Is there a particular name for these things? I see them everywhere. http://upload.wikimedia.org/wikipedia/commons/7/76/Duracraft_pedestal_fan.jpg Thanks!

Thanks uart. Through what you said I have realized that it would far far easier to simply evaluate the polynomials using the cosine-arcosine property, rather than evaluating the polynomials directly. Thanks!