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seen Mar 27 at 11:28

I'm an undergraduate Engineering/Mathematics Student down in Brisbane, Australia. Interested in learning as much as I possibly can about maths, particularly the ideas/constructions/history/motivation behind the classic undergraduate concepts.


Mar
27
awarded  Editor
Mar
27
revised Geometry of Hamilton-Jacobi Equation
added 86 characters in body
Mar
27
answered Geometry of Hamilton-Jacobi Equation
Mar
27
comment Geometry of Hamilton-Jacobi Equation
Actually, I don't think such general solutions could exist in this case, as every solution satisfies $S[\gamma_{ext}] = S(t_1,y_1)-S(t_0,y_0)$. This is a little surprising, but I know so little of the theory of FOPDEs I really have no right to be surprised here :)
Mar
27
comment Geometry of Hamilton-Jacobi Equation
@Qmechanic Thankyou once again! You've been very helpful, and I now feel my initial suspicions were completely vindicated: the converse is true, and solutions of the H-J equation do correspond to the minimal action from some particular point in phase space (or at least elements of the complete solution - there may be general solutions derived from envelopes of the complete solution which behave otherwise.) I'll explain my error (as usual, very silly) in an answer below. :)
Mar
26
asked Geometry of Hamilton-Jacobi Equation
Mar
19
comment What's the interpretation of Feynman's picture proof of Noether's Theorem?
This is excellent, thanks, but I have a question: You say the virtual path $A^* -> A' -> B' -> B^*$ is an infinitesimal variation of the classical path $A^* -> A -> B -> B^*$, but the derivatives of the paths are not close at all. My understanding is that the Euler-Lagrange equations are only necessary for a weak extrema - i.e. the functional is stationary relative to all the curves 'close' to it, where we define 'close' in terms of both the value of $y$ and it's derivative $\dot{y}(t)$. But doesn't your proof assume that we have a strong extrema?
Jan
2
awarded  Teacher
Nov
8
awarded  Tumbleweed
Nov
1
answered Exact Relation between voltage and current
Nov
1
asked Callen's Second Postulate - Composite or Closed+Composite systems?
Oct
23
asked Two Limits in Thermodynamics - Reducing Driving Force and Increasing Resistance
Oct
14
awarded  Popular Question
Oct
14
awarded  Nice Question
Oct
14
comment How did Kelvin make this fascinating calculation?
Thanks, that's beautiful in the terribly-obvious-when-you-see-it kind of way :)
Oct
14
accepted How did Kelvin make this fascinating calculation?
Oct
13
asked How did Kelvin make this fascinating calculation?
Oct
9
asked Is every imaginable quasi-static locus (with non-decreasing entropy) physically realisable?
Sep
24
awarded  Autobiographer
Sep
18
comment Inconsistency between Helmholtz and Gibbs Free Energies
This is probably a terribly silly question, but if two phases are at equilibrium at constant $p, T$ and $N$, doesn't that mean that they have equal Gibbs free energy (per mole), so that irrespective of the fraction of ice or water, the Gibbs free energy is the same single value?