Note 426(1): New Equations of Motion for m Theory
The vector method of Eqs. (24), (25), and (37) to (39) is used to define v sub N squared and p and q. as in Eqs. (31) and (36). The vector Hamilton equation p bold dot = – d H / d r bold = – grad H can be used for example, and divides into the equations for p1 and p2. A similar method was used in UFT417 for the lagrangian using the vector Lagrange equations. Eqs. (40) to (46) use the canonically conjugate generalized coordinates p and q in an entirely standard way, but at the same time the discovery is made of the new equation of motion (46) This can now be applied to m theory.
Note 426(1): New Equations of Motion for m Theory
It is not clear to me if you used v_N in the form (26) througout the paper. If so, we are always dealing with two variables q_r and q_phi. The Hamilton and Lagrange equations are defined for q_i and p_i, one cannot build the modulus of q_i for example and use this in the said equations. What do q and p stand for in eqs. (40) ff. ?
Horst
Am 27.12.2018 um 11:09 schrieb Myron Evans:
Note 426(1): New Equations of Motion for m Theory
This notes uses the full power of Euler Lagrange Hamilton dynamics to derive new equations of motion for m theory and for classical dynamics in general. For example the extension of the Evans Eckardt equations in Eqs. (10) and (11) and Eq. (46), a new equation of motion which seems to have been missed hereto. It is tested on the Newtonian and special relativistic levels and found to be correct. These equations can now be applied to m theory, in particular to energy from m space and its spin connection. This energy can become theoretically infinite in m theory. After that, the formalism can be extended to the Hamilton Jacobi level in classical and relativistic physics and also electrodynamics and other subject areas of physics. The relativistic Hamilton Jacobi equation is described in "The Enigmatic Photon" and in the classic books by Landau and Lifshitz.