## Conservative Fieldgreenspun.com : LUSENET : quaternions : One Thread |

what is conservative field?

-- Waqas Ch. (waqas266@hotmail.com), 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

-- Doug Sweetser (sweetser@alum.mit.edu), June 23, 2003.

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