Conservative Field : LUSENET : quaternions : One Thread

what is conservative field?

-- Waqas Ch. (, June 12, 2003


Hello Waqas:

A concervative force field has four equivalent definitions.

1. The curl is zero. With quaternions, the curl is isolated from other derivatives by using a commutator. If box === (d/dt, Del), and [A, B] === (A B - B A)/2, then for a force F will be conservative if:

[Box, F] = 0.

2. There is a scalar potential function for a force F. This works because Del X (Del phi) = 0. Take the derivative of a M/R potential, and Newton's law results.

3. The line integral of any closed loop is zero.

4. The line integral along different paths is the same.

If one holds, the rest do.


-- Doug Sweetser (, June 23, 2003.

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