Greg P

698 reputation

210

bio	website
	location
	age
visits	member for	2 years, 6 months
	seen	Apr 18 at 18:43
stats	profile views	90

Researcher in biophysics @ Northwestern.

	698 reputation	bio	website		visits	member for	2 years, 6 months
210 badges		location			seen	Apr 18 at 18:43

summary answers questions tags badges favorites bounties reputation activity

152 Actions

suggestions reviews revisions comments badges posts accepts all

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
Feb 3	comment	Can the Lorentz force expression be derived from Maxwell's equations? Can you check the link to your blog?
Jan 13	comment	Entropy of a mass arrangement around the earth Agreed with zephyr, the entropy of the system increases. The height of each grain of sand is only a single degree of freedom. That tiny number of degrees of freedom does indeed become more ordered, but the zillions of atomic degrees of freedom become more disordered.
Dec 8	comment	What are the difficulties and their potential solutions regarding the creation of a functional lightsaber? Given that lightsabers are fictional, doesn't that make this question ill-defined? One might as well ask for a physical explanation for the Force.
Nov 10	awarded	Yearling