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Researcher in biophysics @ Northwestern.


Sep
24
awarded  Autobiographer
Sep
14
awarded  Nice Answer
Sep
11
comment Propagation/generation of sound is an isentropic process
Minor correction: according to your link, it was Laplace, not Leibniz, who corrected the error.
Nov
10
awarded  Yearling
Nov
10
awarded  Yearling
Jun
7
comment why does perpendicular motion to the direction of someone' s approach does not affect the distance between them
Suppose you are a mile directly north of me. At exactly the same time, I take one step towards you (north) and you take one step west. By how much did the distance between us decrease? Basically by one step. Not quite one step, actually (work it out, Pythagorean theorem). But in the limit of taking very small steps (like the bugs that are continually tracking each other) we would be getting closer by one step's distance. Similarly, the rate of decrease of the inter-bug distance is equal to the bugs' speed.
Apr
10
comment Is fire plasma?
A similar question is the basis for a recent project in science communication. Check it out: flamechallenge.org
Apr
10
comment Why is $L^2$ norm of the gradient called kinetic energy?
In quantum mechanics, the gradient operator represents momentum (to within a constant factor). That is why they would call the square of the gradient the kinetic energy (momentum squared, to within a constant factor). That is quite general and not confined to any particular system. But yes, the vector potential is added to deal with the electromagnetic field.
Mar
20
comment Hamilton's equations in terms of initial conditions
Yes, I see what you mean now. The give-away of course is that the equation is not correct as printed in the paper (see pcr's example).
Mar
19
comment Hamilton's equations in terms of initial conditions
The paper explicitly defines $z = {\bf Z(0)}$, and both $z$ and ${\bf Z}$ are used elsewhere in the paper, so I'm still not sure.
Mar
19
comment Hamilton's equations in terms of initial conditions
No, you didn't miss it ;-) I added it after your answer to clarify the question.
Mar
19
revised Hamilton's equations in terms of initial conditions
added 71 characters in body
Mar
19
comment Hamilton's equations in terms of initial conditions
In the paper, $z$ represents the initial values, that is, $z = {\bf Z(0)}$. I still do not see how to get these equations involving $z = {\bf Z(0)}$ from the usual Hamilton's equations which involve positions and momenta evaluated at the same time $t$ as on the left hand side.
Mar
19
revised Hamilton's equations in terms of initial conditions
added 261 characters in body
Mar
19
comment Hamilton's equations in terms of initial conditions
This is the standard vector version of Hamilton's equations. How are these related to the ones in the paper (and the question) which include derivatives with respect to the initial values of p and q? That was my question.
Mar
19
comment Hamilton's equations in terms of initial conditions
Thanks, but my question is specifically about the issue of evaluating the derivative with respect to the initial conditions. In other words, how do I get the "usual" Hamilton's equations starting with the ones in the question.
Mar
19
revised Hamilton's equations in terms of initial conditions
added 283 characters in body
Mar
19
awarded  Student
Mar
19
asked Hamilton's equations in terms of initial conditions
Mar
4
awarded  Nice Answer