Agreed with this, the Hamilton equations give new information when used with the Lagrange equations, and your code for them will be very useful.

426(2): New information about m(r1) from the new equation of motion

There seems to be a typo in eq. (8), it should read partial r dot / partial L at the rhs.

It is important to know that this generalized momentum p_phi=L is different from that in eq. (9) which is that of a general coordinate system (r-phi). If p_phi=L, one has to transform p_phi to a linear momentum having the same physical dimensions as p_r:

p_phi –> p_phi/r

or better:

p_phi –> p_phi/q_r.

This has confused me in some previous notes and in the computer-based calculation of Hamilton equations which is under way.

In eq.(15/16) the middle part is missing a time derivative. The rhs of (16) should have an additional “m” in the denominator to describe a momentum, similarly in (24).

Eq. (30) seems to be valid in the inertial system only because v_N (in 31) has no angular component. Perhaps it would be recommendable to write out the Lagrange and Hamilton equations with coordinate indices as in M&T to avoid ambiguities.

Horst

Am 28.12.2018 um 15:38 schrieb Myron Evans:

426(2): New information about m(r1) from the new equation of motion

The new information is dm(r1) / dv1 = 0. This adds to the information about dm(r1) / dr1 in UFT425. This note explains the discussion with Horst this morning through the vector Hamilton equations (12 and (13) and shows that it is possible to choose p = m v sub N as the canonical momentum whee v sub N is the complete Newtonian velocity . The next stage is the development of the Hamilton Jacobi formalism of m theory. This can be used for the whole of physics and not just dynamics. The quantization of m theory takes place of course through the hamiltonian and that can be tied up with the well known Lamb shift theory of vacuum effects in the H atom. The Lamb shift can be understood as an effect of spherically symmetric spacetime.

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