Section 3 of UFT 420

Many thanks! This is another excellent Section 3 by Horst, showing that the critical terms in the lagrangian and hamiltonian are essentially the same. It will be very interesting to develop H , L and dH / dt = 0 and dL / dt = 0 in quantum mechanics for example and apply them to all kinds of problems in classical dynamics. This is my intention for UFT424. Finding the right lagrangian is also an important problem. In fact the lagrangian L is related to the hamiltonian H as described in the equation following Eq. (14.114) of Marion and Thornton third edition:

L = H – sigma sub i v sub i p sub i

and this is worth investigating further.

Added today

Dave

On 12/7/2018 11:37 AM, Horst Eckardt wrote:
> I finished section 3 which contains various calculations of equations
> of motion. It results that the differences between Hamiltonian and
> Lagrangian method are less significant than thought.
>
> Horst


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