New Formulation of the Hamilton Equations in Special Relativity

This uses the choice (20) of canonically conjugate generalized coordinates and the hamiltonian (33). The choice (20) means that there appear two new equations of motion, Eqs. (22) and (23), which may be solved numerically with the Evans Eckardt equations (25) and (26). It is shown that the Hamilton equations produce the force equation (37) of special relativity, used in previous UFT papers to produce a precessing orbit. So both the Hamilton and Euler Lagrange equations produce the same force equation. In addition, the Hamilton equations give the new equations of motion (22) and (23). To deduce these analytically requires the complete consideration of Euler Lagrange Hamilton dynamics. So the Hamilton equations produce new information not given by the Euler Lagrange equations. Finally the choice of canonically conjugate generalized coordinates (4). when used in the Hamilton equation (41) shows that the angular momentum is a constant of motion. In the Hamilton Jacobi formalism it is therefore defined by the action equations (46) and (47).The Hamilton Jacobi formalism therefore defines the action. The three complete systems of dynamics were traditionally the Euler Lagrange, Hamilton and Hamilton Jacobi, but a fourth system has just been inferred, the Evans Eckardt system of dynamics. All four should be used together for any problem being considered. Their power is greatly amplified by the ability of the Maxima code written by Horst Eckardt to integrate them.


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