Hamilton Jacobi partial derivatives with respect to the constants of
- From: jacques <jacques.fric@xxxxxxx>
- Date: Mon, 7 Jan 2008 13:00:37 +0000 (UTC)
In his 1968 paper on the structure of Kerr fields, B. Carter using the
separability of the Jacobi action found a 4th constant of motion
allowing to determine the geodesic motion in such space time.
For setting the system of the four relevant differential equations he
used the property that "the partial derivatives of the Jacobi action
with respect to the constants of motion are themselve constant".
Where can I find a demo of such theorem?
Along the geodesic where the Jacobi action is "extremum" the constant
of motion are "constant" , but according to the form of the action the
demo is not obvious.
I guess that the action should be written in a form involving only
constants of motion by some transform, in case, the property should be
obvious. In case, how should this transform be defined?
Thanks for some explainations or a link.
.
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