374(3): Equations for the Precessing Orbit of Fluid Gravitation

In the first instance, Eqs. (27) to (29) can be solved numerically using Maxima to check that the method gives the correct orbit (18). Then the algorithm can be modified to solve Eqs. (37), (38) and (40) numerically using a model for the function x defined in Eq. (31). Finally Eq. (44) can be added if the fluid is assumed to be incompressible, so both the orbit and x can be found. The caveat of this note explains why the note slightly corrects the equations of UFT363. The lagrangian method of UFT363 gives Eq. (47), which is different from the correct Eq. (37). The reason is that the kinetic energy of fluid gravitation, Eq. (48), is not in the required format (49) demanded by the Hamilton Principle of Least Action. The kinetic energy must be T(r bold dot, r bold). Sometimes it is simpler and clearer to derive results without the Lagrange method using both the Lagrange and Hamilton or canonical equations of motion.


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