In the March 2024 issue of Nature Physics 'Computing in Physics Education' (https://www.nature.com/articles/s41567-023-02371-2) we read:
"In the USA the undergraduate physics curriculum - that is, the standard set of coursework and activities in an accredited physics major – looks much the same...
Yes, my book .... Mathematical Modeling and Computational Calculus
See also ...
The Coming Revolution in Physics Education
A Revolution in Physics Education Was Forecast in 1989, Why Hasn't It Happened? What Will It Take?
A New Curriculum for Classical Physics
I'll give a controversial opinion .... assuming that the DE module is for a physics program. I'd begin by pointing out that classical physics is based on analyzing differential equation models of physical systems, but that, unfortunately, differential equation models of most physical systems...
I have a couple of playlists .. one for systems modeled by ODEs ...
and one for systems modeled by PDEs -
All the vids follow the same sequence - state the governing laws of physics for the system, model the system with DEs, translate the model to computational statements using Euler's...
"Not sure how universal it is, but my experience through half of my undergrad education gave me the impression that 90% physics was about exactly solvable problems."
Your impression was the result of an illusion. In reality very few problems in physics have exact solutions - even in...
? That doesn't make sense, I want it to be read... even debugged if necessary ...
Generally, things become much clearer when you actually have to program them and check if they work ... For example, it took me over an hour, and many corrections, to get that program to work.
That's not math, that's MATLAB.
In any case, now the question is, why does every book ignore the problem of an analytical solution for the 1-D gravity problem (as noted in the ref. in the wiki article, the guy looked at 100 physics books) and what is the solution?
From the reference in the...
By Jove ! ... and I've only been Matlabbing for 100 years !
G=6.7e-11; % gravitational constant m^3/(kg*s^2)
mEarth = 5.9742e24; % mass of Earth in kg
rEarth = 6.378e6; % radius of Earth in m
mu = G*(mEarth + 1);
y0 = rEarth;
t = 1;
x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))^(2/3);
y1...
Thanks, corrected ...
x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))^2/3;
However, now the apple is falling upwards ...
y0-y1 = ans =
-2.2703e+04
The last term in the series ... 2418092*x^7/62077640625
ans =
0.0028
but ... *y0 = 1.8177e+04
So, it's a long way from converging ... However, as t...
The freefall wiki entry wiki Freefall has an analytic solution for freefall distance in a gravitational field, but ... it doesn't seem to work ... at least i can't get it to work ... here is my MATLAB program to test it ...
clear
G=6.7e-11; % gravitational constant m^3/(kg*s^2)
mEarth =...
I felt the same way a few weeks ago about the anomalies ... but with a few graphs they're clear, and now I like them, they're kind of fun! And Kepler's eq. has an easy graphical derivation ...
For many years Kepler's eq was the only way to plot an orbit as a function of time.
Weird ! I have Thornton & Marion, Classical Dynamics of Particles and Systems, 2008, and it doesn't mention Kepler's equation, and in the section 'Planetary Motion - Kepler's Problem' Kepler's laws are derived but there is no mention of the equations of motion.
I have the first edition, I think, printed in 1965. I downloaded the 3rd edition, Goldstein, Poole, and Safko, and there is a new section that doesn't appear in ed. 1, titled 'The motion in time in the Kepler Problem' where Kepler's equation is covered, and it adds ...
'Indeed, it can be...
I worked at Stanford Telecom and knew a lot about the incredibly complex and precise GPS system, and there was a relativistic correction to something :), I think it was the clock (on the satellite), but I've forgotten the details.
The surprising thing to me is that the books don't even mention...
I have Colwell's book. What I'm wondering is if the, or any, solution is included in any textbook used in the universities. Numerical is fine. None of the textbooks I've looked at even mention the Kepler equation, which is a little surprising to me because of its importance in the history of...