Recent content by l4teLearner

thanks for spotting the typo, I'll fix it. as for the order of derivation and expectation, if you look at the beginning of the paragraph, the value to calculate is the derivative of the average of the distance squared, as we seek to find ##\alpha## in ##<R^2>= \alpha## and prove that it is...

I am studying lesson 41 (volume I) of the Feynman lectures on physics. You can find it at the following link https://www.feynmanlectures.caltech.edu/I_41.html#Ch41-S4 What I don't understand, first, is this consideration: "What is the rate of change of ##x^2## ? It is ##\frac{d...

Thanks again for your patience. Before I dive into the calculations again, I would have two more (requests for) clarification to make. 1. I think the statement of the problem was a bit misleading in this sense: ##\xi, \zeta, \xi## and the parametrization with ##\phi,\theta## are...

Nevermind, that reference is for _linear momentum_, and not _angular momentum_. :) Apparently, the coriolis force that you mentioned causes angular momentum in the non inertial reference frame to be not conserved.

Thanks for your answer. But I am super confused now. What is ##E## for you? If by ##E## we mean the total mechanical energy measured in the rotating frame, I was under the impression that it is indeed conserved, as the fictitious forces measured (if ##\omega## is constant) are conservative. As...

Thanks for the reply, this is the link to the first post of the thread Thread 'Action variables in a non inertial system' https://www.physicsforums.com/threads/action-variables-in-a-non-inertial-system.1079160/ In general, after some time, I am no longer able to edit my posts.

Hello, I have posted a homework help request and subsequently documented my attempts to solve it, in two further replies to it. I have replied to my original request because after some time the original post was no longer editable. But now it appears that my help request has already two replies...

I am assuming that the ##y## component of the angular momentum is conserved. This should be my second integral. I evaluate it as $$L_y=mab[-\frac{p_\phi sin\theta cos\theta sin\phi + abm\omega sin^2\theta cos^2 \theta sin^2\phi}{mb^2sin^2\theta}+\frac{p_\theta cos\phi-abm\omega...

I have evaluated the conjugate momenta as ##p_\theta=abm\omega cos\phi+m(a^2 sin^2\theta+b^2cos^2\theta)\dot{\theta}## and ##p_\phi abm\sin\theta cos\theta sin\phi+mb^2sin^2\theta \dot{\phi}## hence the Hamiltonian, after some algebra, is $$H=\frac{(p_\theta - abm\omega...

I guess the first steps in the resolution of the problem are - to calculate the expression for the conjugate momenta to ##θ## and ##ϕ## - to calculate the Hamiltonian of the problem - to write the Hamilton-Jacobi equation and see if it is separable I struggle in finding conserved quantities...

In the formula above I have that the mechanical momentum of the horizontal force with respect to ##C## is always ##0## because the point of application coincides with the pole. Also, the mechanical momentum of the costraint reactions is ##0## because the costraint is smooth so the reaction is...

thank you! I will attempt the calculations with the lagrangian that you provided and will let you know.

hi anuttarasammyak, thanks for your help. yes, I evaluated the angular velocity as ##\dot \phi - \dot \psi##, it's one of the formulas I wrote just under the picture, in the first paragraph.

I express the total kinetic energy of the body, via König theorem, as $$T=\frac{1}{2}mv_p^2+\frac{1}{2}mI{\omega}^2$$ where $$v_p=(v_x,v_y)=(\dot{r}\cos\varphi-r\dot{\varphi}\sin\varphi-\frac{l}{2}(\dot\varphi-\dot\psi)\sin(\varphi-\psi),\dot r \sin\varphi+r\dot\varphi...

I think we can prove that ##M## is positive definite because it corresponds to the following quadratic form: $$\sum_{1}^{l}x_i^2+\sum_{1\leq i<j \leq l}x_i x_j $$ It can be proved by contradiction that ##\sum_{1}^{l}x_i^2+\sum_{1\leq i<j \leq l}x_i x_j > 0## if some ##x_i \neq 0##. In fact...