Peter Easthope

Hi, In Mod-01, Lec-02, beginning at 54:10 Balakrishnan discusses the "inverted oscillator" having energy 1/2 m qdot^2 - 1/2 m omega^2 q^2. https://www.youtube.com/watch?v=8X1x9RLaaxc Discussed further in Lec-03. Is the "inverted oscillator" only fictitious? If a realization exists, I must have a mental block to imagine it. Thx, ... P.

An instance or example: do an experiment in London, Ontario and the same experiment in London, England. Assuming conditions are genuinely duplicated (or that bias is avoided) the results in the two cases will be the same. Didn't find the source for that but it might be under copyright. This is readily available. https://en.wikipedia.org/wiki/Noether's_theorem Regards, ... P.

I need to study the Lagrangian calculation more. Unfortunately the engineering curriculum focuses on "practical" calculations at the expense of the abstract formulations. Thanks for the help, ... P.

I imagined constancy of mass or masses OK, thanks. I need to understand the Lagrangian calculation better, ... P.

A convenient elementary example: a Newtonian CO2 puck on a level table. Non-zero invariant mass, m. (S) Verification of time invariance: verify that the path is a straight line; verify that velocity is constant. Assume m is constant or ignore it? (C) Conservation of energy: assuming the table is level, gravitational potential is constant. Evaluate (m v^2)/2 over a time sequence and verify constancy. Assume m is constant? Otherwise, how is m measured during motion? The invariant mass is assumed to be constant in S? Also in C? Thx, ... P. Make that "air puck" rather than "CO2 puck", ... P.

Only an interest. Not a necessity. Good point. Several details to understand. More below. Thanks. Definitely helpful. Yes, my understanding is meagre. I don't have a specific context. Just trying to understand the theorem. The conservations, C, involve spacetime and mass whereas the symmetries, S, involve spacetime but not mass. Equivalence requires two implications: C => S and S => C. C => S entails removal of mass. S => C entails introduction of mass. The presentations I've seen avoid attention to mass. I'm not claiming that's incorrect; only that I'm interested to understand the involvement of mass better. Thanks for the feedback, ... P.

Hi, How can Noether's Theorem be reconciled with dimensional analysis? For example, invariance under spatial translation is equivalent to conservation of momentum. Spacial translation has no involvement of mass but mass is essential to momentum. How can the invariance independent of mass be equivalent to conservation of a quantity where mass is essential? Thanks, ... Peter E.