Basics of the Lagrangian Method

The fundamental reason for the last note is that the Hamilton Principle of Least Action, from which is follows that the lagrangian must be defined as T(r bold dot) – U(r bold). I will explain this in another note to be distributed shortly. This method holds for any r bold dot. The method used in UFT363 did not satisfy the fundamental criterion for a lagrangian, which is why it did not lead to the correct momentum. The new method of UFT374 corrects this and leads to soluble sets of simultaneous partial differential equations. The new advance is that these can be tied in with the equations of hydrodynamics in many interesting ways. for background reading I suggest Marion and Thornton chapter five. So UFT374 will develop in this way. I recommend Marion and Thornton as far as it goes. It is now known that its section on the Einstein theory is wildly wrong. This was again shown by Horst’s numerical methods combined with analytical methods. Marion and Thornton is not easy, but is recommended reading. I remember doing lagrangian theory in the second year mathematics course at UCW Aberystwyth. It i snot easy, but sometimes useful. I have used it many times throughput my research career. Sometimes it is better to use other methods. The method of UFT374 uses all the available dynamics, Lagrangian and Hamiltonian. UFT176 on the discovery of the quantum Hamilton equations, is now a famous paper, a classic by any standards. There is a hugely successful combination of analytical and numerical techniques in each UFT paper, mainly by Horst Eckardt, Douglas Lindstrom and myself, and many contributions by other Fellows.

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