Relativistic Hamilton equations
These results look interesting and can be integrated with Maxima, giving a lot of new techniques. The Hamilton and Hamilton Jacobi equations can be used in any frame of reference. The rule for going from the inertial frame to any other is as follows. In the inertial frame
r double dot = – mMG / r squared
To transform to plane polars use
a bold = (r double dot – r phi dot squared) e sub r
+ (r phi double dot + r phi double dot + r dot phi dot) e sub phi
so we get two equations as in several UFT papers:
r double dot – r phi dot squared = – mMG / r squared
and
dL / dt = 0
The extension to special relativity and m theory is given as you know in UFT415 onwards. . Having used the Hamiltonian method to get the first equation above we know that all is OK. Your previous use of the inertial frame in several papers is also correct. The most powerful equations are our own new equations, dH / dt = 0 and dL / dt = 0. This is because the code can integrate them to give any kind of result.
(r double dot –